Your answer is made up out of many different questions ans assumptions. I'll try to address all of them individually.
Every Jaqen we saw wanted to help Arya.
That's not true. No Jaqen has ever seemed uncharacteristically helpful to Arya.
- The first Jaqen, the one who Arya frees and ends up giving her the coin, gave Arya three wishes because she saved three lives. Jaqen even explicitly says that because Arya took three deaths from the god of Death, she must provide three deaths (to make amends with the god of death). Jaqen is not trying to help Arya, he is trying to appease his god.
You could argue that Jaqen could've killed three people himself and did not need Arya to help him. However, he may have noticed that she would be worth recruiting, which incentivizes him to give her a taste of what an assassin's life looks like. And it worked, because Arya was impressed by Jaqen's abilities as an assassin (she had been wanting to learn similar skills, and it shows in her behavior).
- Jaqen (who first looked like the old black man) took Arya in as a recruit, because she asked to train with them. The Faceless Men need bodies, just like how an army needs soldiers. Of course they are going to take in recruits. This is not a selfless act.
- Jaqen kills himself in front of Arya, to prove the point that no Faceless Man has an identity. This is part of Arya's training.
- Jaqen teaches Arya in the ways of the Faceless Men. Again, this is not a selfless act.
If anything, the opposite of your claim is true:
- Jaqen willingly sends the waif after Arya. Jaqen had already noticed that the waif carried resentment towards Arya. Sending the waif shows that Jaqen was not in any way trying to keep Arya safe.
I think your argument is based solely on the last interaction between Jaqen and Arya:
- When Arya states that she is Arya Stark of Winterfell, Jaqen gives her a subtle smile and implicitly agrees, allowing her to leave the Faceless Men and resume her life as Arya Stark.
It's never really revealed why Jaqen responds the way he does. It's likely that he simply accepted that Arya would never be a Faceless Man (as she is much too connected to her identity).
If the Faceless Men could force you to lose your identity, then Arya's training would've been pointless, they could've simply made her forget who she was. The only logical explanation for needing to train Arya is that Arya needs to voluntarily let go of her identity.
And if Arya then is shown to stick to her identity, then she is no longer a viable recruit.
Jaqen is not incapable of emotions (evidenced by his somewhat humanlike behavior when Arya meets him in Westeros). He is capable of showing emotions, but as a Faceless Man he chooses to not display them.
His subtle smile at Arya may have been a "leak", where he couldn't hide his approval of Arya's decision. He may already have realized that Arya's destiny is not as a Faceless Man, but Arya herself did not know this until she explicitly restated her identity (thus causing Jaqen to smile, because Arya finally gets it).
How does Jaqen keep on having the same intentions while another faceless man wears him?
This question is built on the assumption that Jaqen's actions are personal, and that they are a kindness towards Arya.
But this is not the case. Jaqen's motivation has always been the Many-Faced God. He is doing the bidding of the order of Faceless Men. His actions are not driven by his personal decisions.
If anything, the whole point of Arya's training is to not let your personality interfere with your service as a Faceless Man. Arya is explicitly forbidden to decide whether she should kill her target or not.
If Jaqen is a skilled Faceless Man (which he is), that proves that his decisions are not made by himself, he is merely executing on the will of the Many-Faced God.
This explains why every Jaqen always behaves the same way: all Jaqens are merely doing what the Many-Faced God tells them to do.
There is Jaqen who is willing to help Arya and then there is Waif who doesn't accept her. If they chose to swap their masks, they would also swap their "minds".
I agree with your facts, but not your conclusion.
If we focus on the lore, the Faceless Men are nothing but empty vessels who do the bidding of the Many-Faced God. This means that all Faceless Men (regardless of the face they wear) must behave in the exact same way.
This is similar to ants. They have no sense of self-preservation, everythnig they do is for the colony, their common ideal. Faceless Men do everything for the Many-Faced God, and therefore share the same ideals.
Thinking about it logically, the TV show could have shown a different face for every single scene where a Faceless Man was shown. This would not have changed the plot in any way, since every Faceless Man should behave the same way.
However, we must also understand that a TV show uses TV tropes. Continually introducing new faces would have been incredibly confusing for the viewer to follow.
So instead, the show runners chose to retain consistency (for the viewer) by reusing the same faces. The face we know as Jaqen is the "convinced" Faceless Man (the one who sees Arya as a viable recruit), the face we know as the waif is the "unconvinced" Faceless Man (the one who sees that Arya is not really a Faceless Man).
We've seen one other noteworthy Face: the old black man who opens the door for Arya. This face has been neutral and devoid of emotion, which is much closer to how all Faceless Men should behave.
I am aware that the waif was not a Faceless Man yet, but a recruit just like Arya. However, the waif has all the skills of a Faceless Man, and behaves as if she is already part of the order (with one exception: she doesn't sense her own personal resentment of Arya, which becomes her downfall).
The waif is still Arya's superior, which is the only relevant part of my argument. From Arya's point of view (and by extension, the viewer's point of view), the waif is a representation of the order of Faceless Men.
Jaqen and the waif visualize the duality of Arya's state of mind. On one hand, she wants to forget her life and what she has had to suffer through (Jaqen - Arya wants become a Faceless Man). On the other hand, she wants to take revenge on those who wronged her, which means that she doesn't just want to forget the past (the waif - Arya does not want to become a Faceless Man).
Here's an interesting (somewhat offtopic) idea:
Jaqen subtly smiled at Arya when she stated her identity (and her intention to remain Arya and not become no one). It makes sense for the waif to smile here, because Arya has just confirmed what the waif always knew about Arya: she's not a real Faceless Man after all. Maybe Jaqen's smile is actually the waif's smile.
If you ignore the face (which you should really do for the Faceless Men), then the smile becomes more meaningful: it showcases a general approval by the Faceless Men (both those who saw her as a viable recruit and those who did not) that Arya is not going to become a Faceless Man.
The duality inside Arya has disappeared (she has chosen to remain Arya), and the dual faces have also disappeared (as Arya has killed the waif). This seems like it's clear symbolism that refers to Arya's state of mind.