Teddy (Joe Pantoliano)’s Timeline and Summary

Speculative: Teddy is a policeman assigned to Leonard's case.
Teddy believes Leonard and helps him track down the missing John G. and kill him.
When Leonard doesn't remember this, Teddy repeats this in different cities using different John or James or Jimmy G's as the targets.
In this particular city, Teddy calls Leonard on the phone a lot, listening him talk about Sammy Jankis and also suggesting information about a local drug dealer who might by John G.
Leonard meets Teddy in the Discount Inn lobby and Teddy tells him where Jimmy is going to be.
After Leonard kills Jimmy, Teddy shows up and pretends not to know Leonard until Leonard hits him over the head with his camera.
Teddy tells Leonard everything about his unremembered and misremembered past (or maybe a bunch of lies; it's unclear).
Teddy shows up at Emma's Tattoo parlor and tells Leonard he's a snitch and that some cop is messing with Leonard.
He shows up in Leonard's car outside of Natalie's house and warns him against trusting her.
He helps Leonard get rid of Dodd.
He buys Leonard lunch and reassures him of his purpose, and that he is indeed alive.
He shows up at the Discount Inn again and lets Leonard drive him out to the same abandoned building where he killed Jimmy.
Leonard hits him on the head and pulls a gun on him, but Teddy isn't afraid until it's too late. He calls him a freak.