If you open your social, friend's page, beside the Friend's list is a second tab. If you click on that all inventory items display. You can do a search by keying in several letters of the item you want. If you click on the item it will be added to your list.
I do suggest making the expenditure so you can have 4 items on your list.
jEMSW......When the Puzzle feature was introduced, somehow it affected the social page of iOS users.....it wiped out the items we had put in our wish list and it rendered our private room inaccessible to other players (they get a message that this friend does not have a private room).
The mailman delivered a message to all iOS players and a fix was also posted to the forum, but many iOS players still have not recreated their wish lists.....also, some just read the first part of the mail message and didn't apply the fix to the private room.
The OP is just telling that player that they still have no wish list.....most likely, that person is sending out gifts and wondering why they have received nothing in return.