It's been a bit since I watched Charlotte, but if I remember correctly, in the first episode, when Yu is given the fake test by the student body of Hoshinoumi Academy, he attempts to cheat as a last resort, possessing Jojiro to attempt to get the answers. Needless to say, this doesn't end up working. It is later revealed that Yu's ability is actually to steal abilities, "Loot." Doesn't this mean that he would have stolen Jojiro's teleportation ability? Is this just a plothole or is there some reason that Jojiro keeps his powers?
Rewatched the first episode and I can definitely say that there is no plothole, at least to the incident you were referring to.
In Episode 1, when Yū took the test, the unnamed student council president was supervising him. Yū possessing him has no effect as the unnamed student council president has no power at all. To clarify, it was not Jōjirō who was watching over him while taking the test.
Furthermore, during the episode, he never possessed Jōjirō so no, there was no way he could have stolen Jōjirō's power.
By the way, Jōjirō's power is not teleportation but rather,
the ability to charge at extremely high speeds in one direction.