Oddbean new post about login | logout Yes because Alice's ecash token would be redeemed for sats that would be paid over lightning network from minibits ln node to enuts ln node which would then issue Bob ecash tokens that are kept on his device
If Alice and Bob share the same mint then they can send ecash to eachother without a lightning transaction and with near perfect privacy
iiuc, Alice & Bob can send the bearer tokens amongst eachother intra mint with no Lightning tx but to send inter mint; the token has to be redeemed by the Alice's mint, sats sent via Lightning tx to Bob's mint, and there new bearer tokens are issued to Bob.