In Avengers: Endgame Thor took his hammer from the Asgard in the past and brought it back to the present. So, does Thor from the past use present Thor's hammer after present Thor brought it to the present?
Past Thor does use his hammer because Captain America has returned it to its original place and time by the end of Endgame.
When Captain America volunteers to return all infinity stones to their timeline, he also takes the Mjolnir as well. Since it is returned to its original time, past Thor can use it.
The final moments of Endgame show Captain America going back in time to put the Infinity Stones and Mjolnir back in their rightful place