Acer has an interesting way of defining model lines and specific models. R15, R14, R13, R11 describe the "R" model line and the screen size. And it keeps changing to confuse the natives. Further the the actual Model number is more complex:
First digit (R) indicates the series
Second digit incates the level (7- best, 1-basic)
-
Third digit screen size (7-17.3, 5-15.6, 4-14", 3-13.3", 1-11.6")
rest define the CPU, battery, touch, etc.
So my R11 is really R3-131T-Pxxx and your Acer Aspire R13 aka R7-371T-59ZK is a top of the line unit with a 13.3" display (think I gave you the part number for the 15" display (R7-572) earlier.
The not-so-good news is that I do not show just a rear cover for a R13, just the whole cover and display module 6M.MQPN7.001 or 6M.MQPN7.003