Archie misses him more, now that he knows for sure what he's feeling. Now that he suspects the same is of Horatio. It means that almost as soon as they're separated, he's sending a letter his best friend's way.

He'll keep writing him until they're together again; somehow, he'll manage not to be too obvious about his crush.

(Which isn't to say he isn't hinting. He can let Horatio grow into it while still laying the groundwork, right?)