The Marauder's Map was last seen in Harry's possesion during Deathly Hallows.
What child did Harry give the Marauders Map to, if any?
Apparently, James Sirius Potter stole it (Lived up to his name, li'l boy!)!
[ Ref ]
Courtney: What child did Harry give the Marauders Map to if any
J.K. Rowling: I've got a feeling he didn't give it to any of them, but that James sneaked it out of his father's desk one day.
According to The Cursed Child
Harry had the map under lock at least during Albus's third year, since he was able to loan it out to Headmistress Mcgonnagall.
I assume that he didn't give it to anyone, he just kept it as an old souvenir.