Do you create Link via code in each room? Or have you placed an instance of Link in each room? Or do you have a persistent Link?
Either way, you can do this in the Room Creation Code. In the House room's RCC, set global.house to whatever value means he's in the house.
Then in the Outside room's RCC, check if the variable equals that value, and if so, do either:
instance_create(x_pos, y_pos, objLink)
If a Link doesn't already exist in that room, or:
objLink.x = x_pos
objLink.y = y_pos
If Link already exists or is persistent.
The x_pos and y_pos should be changed to the position you want Link to appear at.