I don't think it's a good idea. We don't the sales directly (you are purchasing from Esellerate), so I cannot say for sure if there are security checks when purchasing using name/address detail of a person, with the payment of another one.
And think about other potential issues like sales taxes: the person you want to give the product might reside in a different country, with sales taxes/VAT at different rates, so it will be quickly a big mess.
So, in general, this is not going to work very well. I suggest to contact us in private.