Sixty-four

@cpw - I did (sorry @chemi ).. But it's too cryptic for my little brain. In fact, if you and @Block builder hadn't mentioned another solution, i would believe I already have the intended solution (my 3rd solution)!

Spoiler: intended solution

Move B to the first block that R walks to (for B 1 to the right, 1 to the left).
B wants to walk away from here. He will use the stairs, instead of walking straight to the other side. But before he leaves the block, stop his movement by clicking far away on the background.
Let R make a full round. He will walk back and forth next to B.
Move B to where R started. Move B again to the square where he wants to get away from, but only at a moment that R blocks the stairs B usually goes to. Instead, B will now choose the other escape, to the other side of the level.

@Block builder - hmmm...

Spoiler

I can get to the point in your spoiler where "R walks back and forth next to B"...

But then i get unstuck. Can you please confirm the numbered blocks above : "Move B to where R started (s1). Move B again to the square where he wants to get away from (s2), but only at a moment that R blocks (s3) the stairs B usually goes to (s4). Instead, B will now choose the other escape (s5), to the other side of the level."..
s1=1
s2=2
s3=?
s4=4
s5=9
My R never gets to 5,right?

@cpw - yes! (or rather, it is for my 3rd solution)

@trids Nice image, this is easier talking.

Spoiler

s3 = 4, you need to push R to 5. Sometimes a few times, depending on timing and R's rotation. R will walk back and forth on 4 and the unnumbered square down those stairs.

@Block builder - Aha!

Spoiler

Thank you.. I couldn't figure out how to swap B and R by getting R to block 5 .. And then I finally understood what you meant by "push R to 5" !

Quite a tricky solution - i don't think I would have found it without your help. Well done, and thanks for your patience! Your 5 stars (even more!) are well earned.

These descriptions are always difficult.

Btw, I still did not manage to get R past the zapper as some of you did. Kept hitting the stairs next to it like crazy...

And now I just managed to do that... . I think I had the rotor in the wrong position.

Btw (again), to get R ontop of the rotating movable consistently, start rotating while R is under the rotor. Then he kind of sticks to it.

Spoiler: The zapper route

First kick R out of the game with the rotating draggable. Then, with B on his initial stone pillar, tap on the wedge by the zapper. As he arrives there, tap the stairs. And as he jumps to the stairs, tap the block just past the stairs. Sometimes he gets stuck, so keep encouraging him by tapping on that block after the stairs. If he won't budge, then you can often safely send him back to the pillar and try again.

Such amount of activity in this level motivated me to resume the search of the designed solution and at the end I think I found it.

Spoiler: Am I correct?

Move B to the tile with claustrophobic so it modifies R path. Using the rotor push R to the corner cylinder tile when coming back and very quickly get B bewteen the rotor and R. With ability and some luck B gets over R and then on top of the rotor...

Haha, nope. Sorry. There isn't any ability required. Just claustrofobia related logic. Up to the word 'cylinder' you are doing it correctly. The ability stuff thereafter is not required.

Spoiler: Abilty

I had tens of tries to push R to the cylinder avoiding him to turn and go down the stairs, and also to push B against R to climb on top of him. I think do it correctly and fast required good ability, right?

@chemi

Spoiler

That way requires a lot of ability indeed, I did not succeed yet that way. Why don't you let R walk down the stairs? He likes the water.

@chemi - it sounds like you have found yet another solution...

Spoiler

... With B on top of R?

Nice work, but the intended solution is well worth finding - don't give up!

@Block builder - your intended solution uses a trick that's new to me, and I think I need to feature it in another tutorial. Is it your own discovery?