usually the funds show up in your wallet as soon as the transaction that you broadcast from your initial wallet is “seen” by the node that your other wallet is connected to, even if it is still in the mempool. Then the transaction becomes spendable by your other wallet once it is picked up by a miner that adds it to a block in the blockchain and reaches a certain number of confirmations that is determined by your other wallet. A lot of wallets allow funds to be spent after 1 confirmation now tho