Imagine that you throw a ball at another person and that they catch it. This person will give you a boost of momentum. He will need very long arms to catch the ball.
The proton emits a photon, which is moving away from the electron. This photon is then absorbed by the proton, which accelerates it towards the electron. The photon is in a very uncertain position, so it’s not the proton with the long arms. It can transfer its momentum to the proton even if it moves away from it, even if it is moving away from it.