The wallet doesn't keep transaction before joining or doesn't have feature to show it to user.
The sender's wallet will keep that transaction, because wallets by default keep transactions created by their users. The receiver's wallet will see that transaction in the blockchain, unless that receiver will decide to spend it without any confirmations.
If the recipient doesn't have technical knowledge (usually customer service without proper training), he'll reject it because it's not on blockchain.
It will be removed from the blockchain only in one case: when that recipient will spend it. By the act of spending that transaction, the receiver shows everyone that it is aware of that transaction, accept it as valid, and is the owner of that coins.
To sum up: it will be quite easy to prove that transaction happened, because there are only two cases:
1) recipient does nothing and its address will be included in the blockchain (so proving that coins were sent is trivial)
2) recipient spend that coins and the spending transaction can be seen by everyone (including the sender)
Also, in case of blockchain reorgs, the chain can actually get smaller, because if there are two matching transactions in two separate blocks, then they could be replaced by a single transaction in the final chain.
