Good evening. I can do this for you fast, straight-forward an with good communication :) I have plenty of experience (over 15 years) fiddling with websites and PHP and have invented hundreds of tailor-made solutions in that time...
I propose to write a small PHP script to be run from server B, fetching all the images from server A and storing them on server B.
Best regards,
Håkon M. E. Sundaune
Oslo, Norway