Let me elaborate. He won the auction of the item but wants to pay for the item not through eBay because his "app" on his mobile needs "updating" and won't let him finish the transaction on here.

If he can connect to the internet to USE the app in the first place, then he can definitely update the app. Thus the excuse is bogus.

If he wants to pay via Paypal, he can use the Paypal App and then select "For Ebay Purchase". This will link the payment to to eBay purchase, just the same as if he'd gone through eBay Checkout.

If this is something of low value, then I wouldn't worry too much. But if it's a $2,500 computer or something, then I think you need to be extremely cautious. I am not saying it's 100% suspicious, but I just have an odd feeling about it.