Fleet transfer does not appear to be an intended game mechanic in Anacreon (aside from transport capture), but some situations can result in fleets being transferred from one player to the other.
The fleet capture bug has already been noted.
Transports can be gifted by landing them on an unimportant world and encouraging another empire to capture it. If the "gift giving" empire is larger than the recipient, this creates a hidden state of aggression between the two empires that allows the large empire to attack the smaller one without social order penalties.
When an empire abdicates, any of its fleets orbiting a foreign world are transferred to the world's controller. This could hypothetically be exploited in the early game by players who use duplicate accounts to start new empires until they find one near their empire, move the starting fleets to their capital, rinse and repeat until they have an unusually large starting fleet.
Empires that have lost most of their worlds but retain large fleets can choose to move their fleets to another empire's world and then abdicate in order to gift all these ships to the other player.
If fleet transfer occurs on empire destruction, it can create an unbalanced situation where fleets are transferred to a hostile power. If a destroyed empire has fleets orbiting their enemies' worlds at the moment of their destruction (which is likely to be the case if the war is especially vicious), their enemy receives all of these ships when they take out the last capital.
If fleet transfer is intended to be in the game, there should be a formal mechanic for doing so. If not, systems that result in player-player ship transfer should probably be removed.