In theory it is quite simple, if you have the private key that unencrypts what ever is encrypted using 1K83foH3zcUnm1gpLXVKYda4r1vSwE1VXh, then you own those bitcoins.. the thing is doing this test can be a relatively difficult task...(technically speaking). You could try encrypting some words... and trying to unencrypt using the private key... maybe someone with a better technical background can help!?
not sure I follow you agustinfl, however my coins did just show up in my wallet....