What is the result of call to "
https://brd.com/x/gift/someBase64String....."?
I may be wrong, but I think the information encoded in "someBase64String" are not sufficient, if they store information about sender, recipient and amount on the server side.
I'm already out of my depth with respect to sniffing the HTTP between the hosts. If this seems fruitful, I'm open to suggestions for same.
A simple curl

on the URL
https://brd.com/x/gift/VDkzQVozZjFMbVBQbktiUXJSaFZENEZERWhNTTFVMVVmWFFickI2WktkWGNBSFd6b0dhQQ==
Regarding the additional info you suggest, I do have the (current & former) address of the BTC funds, txid (amounts etc.)