In episode 9 we can see the robot operating the wrecked alien ship to take the engine. Then it returns to the Jupiter on the chariot (episode 10) so it's the robot to put the engine there.
This was done under Dr Smith's orders. Remember that when this happens Dr. Smith still doesn't know that Will found the fuel for the Jupiters so she's still looking for a transport to escape from the planet. She believes that with that engine on the Jupiter she may eventually take-off and escape.
Well she's not completely wrong after all, as we can see at the end of episode 10 that the engine creates a worm hole and it uses the Jupiter to fly through it.
I guess those engines have been developed by the aliens to escape their world which is eventually about to be destroyed by the two merging stars (the ones we can see in the last scene). That's why they sent the robots to recover the Resolute engine.
The same happens to the Resolute at the beginning of the story. It looks like that it's the alien engine to create the worm hole in which they all fall in.
I guess that in Season 2 we will see the Resolute again.