Yes.

They provide transaction id.

Anyone can see a transaction was made, just not who or amounts.

You, as recipient, can verify amount.

They, as sender, can prove they sent to your address via tools built into wallet.

There are plenty of guides online for both of you to follow. Have the sender provide you with the transaction private key to be able to verify the transaction.

You should wait 10 blocks (20 minutes) before considering final as you cant spend your funds received before that.