The inside-outer (IO) is a player who prefers to run around his backhand and use his aggressive forehand cross-court against his opponent's backhand. (see graphic 1: player A is the inside-outer)

You might obviously be tempted to push your strokes more and more wide to his backhand but he still runs around the ball and keeps blasting balls to your backhand. And the more you try to hit wider to his backhand the more you miss and your frustration increases. 

What you actually have to do in order to open up his weak side (backhand) is to hit the ball to his strength first… Exactly, in order to open up the weakness, hit it to the strength first. (see graphic 2)

By doing that (sending the ball to his forehand) you will create an opening on his backhand side (assuming that it is his weak side). From there on, you will be in control.

How to execute it:         

I would suggest taking the ball on the rise with your backhand, with heavy topspin, and going down-the-line. You must make a note that changing the direction of the ball will not be easy therefore your aim should be well inside the opponent's singles side line - give your shot a plenty margin for error. 

Returning with a slice backhand (under-spin) down-the-line and short into the court is also a good alternative considering that this will bring the player well inside his baseline, giving him less time to recover and run around his backhand.