Yes, you can. During the purchase of Amazon Pay Gift cards, you will be asked specify the mobile number of the Amazon Pay wallet of the receiver. The receiver's mobile number should be linked to a valid Amazon Pay Balance account and the receiver can be you or anyone you intend to gift the Amazon Pay Gift Card(s).
Once the transfer is initiated, the amount will be added to the receiver's Amazon Pay Gift Card balance. This purchase transaction is not reversible so make sure you enter the correct mobile number and amount.