A few thoughts, please correct me if I am wrong:
(1) Transactions could contain a block number so it would be impossible to put a transaction in a later block, and generate a proof for it.
(2) If A doesn’t receive the merkle information from the byzantine chain, she could exit before the new block is finalised in the parent block.
(3) We assume it is A’s responsibility to pass on the merkle information to B.
I guess such a scheme might then require proofs of non-existence for withdrawals in the parent chain.