Did they (Kraken) give you the transaction hash/id?
If they did, then follow BitMaxz's suggestion by copying the hash and looking it up on a block explorer to verify that the transaction has already been broadcast and to retrieve the recipient address . Then check if that address belongs to your wallet.
To do this, open Electrum, then go to the
addresses tab. You should see the receiving address from the block explorer on the addresses list on your Electrum.
If the transaction has been confirmed and the address does indeed belong to your wallet but your wallet doesn't reflect the actual balance then, most likely, your wallet is not synced or you are having a connection issue.
If you truly sent it to your Electrum wallet without mistake then its probably sitting on the mepool waiting to be mined,if the fee is not too low although mempool not congested.
Electrum shows unconfirmed transactions on the history tab and updates the balance accordingly by default. So, this can't be the reason why he can't see the transaction on his wallet.