The ornamental design for a back cover for displayscreens with power distribution, as shown and described.
1. Back cover for display screens with power distribution
1.1: Perspective
1.2: Front
1.3: Back
1.4: Left
1.5: Right
1.6: Top
1.7: Bottom
In the center of the claimed design, there is a power distribution unit that distributes power to multiple displays; the broken lines indicate portions of the article that form no part of the claimed design.