Case one: you control the address
If you sent to your own address — the usual case when moving between your own wallets — the funds are at the same address on the other chain, and your key controls it there too.
Add the network to your wallet, add the token by its contract address on that chain, acquire a small amount of that chain's native coin for gas, and move the funds. Annoying, not lost.
Case two: an exchange deposit address
Exchange deposit addresses are frequently contracts or are only monitored on specific chains. If the exchange supports that chain and that token, support may be able to credit it, sometimes for a fee. If it does not, the funds are typically unrecoverable.
This depends entirely on the exchange's internal tooling. It is a request, not a right.
Case three: a contract address
Sending tokens to a contract that has no function to retrieve them leaves them permanently stuck. The contract owns them and nothing in its code can move them out.
This is the usual outcome of sending to a token contract address instead of a wallet address, and it is final.
Prevention, since recovery is unreliable
Verify the network on the sending and receiving side every single time. Send a small test amount for any first transfer to a new destination. For exchange deposits, use the address the exchange shows for that exact network, generated fresh.
FBT Swap shows the selected network before each signature. That display is the last checkpoint before an irreversible action.