Can I move a player from one team to another inside a league?

Yes, but there is no transfer button. Do it in three steps:

• Remove him from team A’s season roster (League, Participants, team A, Remove).

• He must be a member of team B: B’s owner or captain invites him and he accepts.

• Add him to team B’s season roster (League, Participants, team B, Add).

Matches already played keep their lineups and stats; he goes into team B’s upcoming matches. A player can’t be in two teams’ rosters in one league unless the league has “Players in multiple teams” on.