Well, that's exactly what I thought. Actually, there is no such information about the recipient on the postcard.
The interpreter might misread the right end column as 其の後長らく御無事, but actually it's 其の後長らく御無沙汰致し居りますが, i.e., the writer just apologized for not keeping in touch with the recipient(= his older brother) for a long time. Or, the interpreter might refer to the second line; 兄上にも御元気に軍務に御精働の事と存じます. This is just the writer's hope/guess, something like "I think you must be in good health and...", thus, it's a typical greeting used in a letter. It's indeed just personal information, though.