Vrftsjtryk

In Avengers: Endgame, Thor brings back Mjolnir (his hammer) from the past to his "future" self through the quantum tunnel. Later in the movie, Captain America gets hold of it being worthy.

However, I don't remember if Cap takes it back to the past in the climax. If he doesn't - that would break the spacetime continuum, Mjolnir being destroyed in the past.

If he does bring it back, how come he knows the exact time and place to return?

Cap probably brings it back to the past.

I can't provide a picture, but Mjolnir is seen at his side when he goes back to place the Stones in the past, and it's nowhere to be seen when he gets back. I think he knew that thing had to be given back to time, to preserve the original "continuity", and did so.

As to when and where to return, it's not that hard to figure out: ask Thor when he picked it up, go to that very moment, sneak anywhere on Asgard, drop Mjolnir on the ground, go back to Peggy/the rest of the Infinity Stones. Past Thor can summon Mjolnir at will, and probably isn't that much regardant of where he left it - the hammer will just zoom into his hands.

Steve takes Mjolnir back into the past with him, you see it on the floor of the platform. Presumably he takes it back to Asgard, but, he could equally well as keep it for himself... we simply don't know what he does with it.

If he does bring it back, how come he knows the exact time and place to return?

It is safe to assume either Thor or Rocket told him the time this happened.

Well... have you wondered why did it take a while for Mjölnir to reach Thor when it was summoned? Maybe once when it took longer than usual it was because Cap placed it somewhere a little far away when he jumped back in time one last time....

And most importantly, Banner made it clear that your past doesn't and can't change the future in which you are... although that was contradicted when Cap showed up again as an old man... that too with his shield, all shining and new.