story about looking for reincarnated loved one?

Without spoiling anything more, that’s what I Origins is about.

I haven’t seen the movie, but I believe Birth (2004) hits on this theme:

Not that much. She wasn’t looking for her husband until

the brat claimed to be him

Karen Russell wrote a short story called The Barn at the End of Our Term. In it, Rutherford B. Hayes (as well as several other U.S. presidents) were reincarnated as horses in a barn, and Hayes-the-horse began to suspect that one of the sheep in the pasture was his reincarnated wife.