See following image. Who is Run-out?
A is crossed the crease and B is crossed half of the pitch. Run-out happening in B's side. Then who is out? A or B?
B is out. The batsmen haven't crossed each other and B is closer to the end where the fielder puts the wicket down.
From the wikipedia Page
Another Reference.Check the 3rd Point
It is not a question of which batsman has covered the greater proportion of the pitch, but rather it is a question of whose is the ground where the wicket is put down.
In this case, B's is the ground where the wicket b has been put down. Therefore B will be out.