Borden sent Angier to Tesla as a misleading fake clue, but why did Tesla knew about the machine Angier was talking about if it was just Borden's crazy idea to mislead Angier?
Or even if he didn't know and just made such machine for Angier... Is it supposed that Borden just had the crazy idea of a teleportation machine and Tesla was just casually working on the very same thing?
Borden didn't account for Tesla actually building a working clone machine.
Tesla is a very eccentric man. It's in his behavior, but anyone who heard what he was working on or experimenting with would similarly conclude that, and assume that he's chasing a pipe dream, no more than an alchemist trying to turn lead into gold.
It makes no sense for Borden to send Angier to Tesla in the knowledge that Tesla had a working machine. What makes much more sense, is that Borden tried sending Angier on a wild goose chase by convincing him this "obviously hopeless" inventor was trying to build the impossible.
Angier, driven by his need to learn Borden's trick, would likely spend a lot of time before he'd realize that Tesla was a fake lead. He has every reason to believe that Borden's code was supposedly real, and Tesla actually talks about trying to invent the exact technology that would explain Borden rather inexplicable trick.
Keep in mind this movie takes place in the 1800s, and how long Angier would have been away from London, giving Borden a lot of time to become unrivaled by Angier. This mostly works, when you consider that Angier had to reintroduce himself to the stage upon his return. Had he not had this amazing new trick (which seemed likely to Borden, since Borden didn't account for Tesla actually building a working clone machine), Angier would've been lagging behind Borden for quite some time.