I must admit when I took a quick look at both signatures, the signature on the picture sleeve didn’t get a second glance. Now that Ballroom has opened my eyes I can see that it does look to be signed by John. The Peace and From perhaps seal the deal.
The sleeve is very nice indeed. You can also tell by the number of "thesaleroom" watchers (currently 16) that it is considered real by the market. Having said that, the other one also has ten watchers, six bids and is currently at £425.