Reading a 10 pin 7 segment (2 digits) sing Arduino 1. Please Help!
Your display is multiplexed, so you will need to monitor not only the segment lines but also the digit lines.

First figure out if your display is "common anode" or "common cathode" as the logic in one case will be inverted from that of the other.

For your test case, you can write the driving and reading arduinos to the display in the same way, but configure all the connected pins on the reading one as inputs.

The tricky part is going to be detecting when the segment select has changed, but you could do it by storing the current value of each select pin, and then reading the new value.  If you see that the old value was inactive and the new value active, then wait a tiny amount of time and read all of the segment lines.  You want to wait long enough to make sure that the data lines have been driven to match, but no so long that you get the data for the next digit instead.  If you have access to a scope, you can find the best value, but you could also experiment by making the delay short until you get wrong data, making it long until you get wrong data, and then picking an intermediate value.

You may find it easiest to read all 7 or 8 segment lines into a single byte value, and then compare it to each element in the lookup table you used in the driver code until you find a match.

If you don't know the exact wiring of the segments on the unknown target board, consider printing the bytes to the serial monitor as you cause the displayed values to change (cup of ice water, cup of hot water...) and taking notes of the segment values vs. the digits you see display.  It will be a puzzle, but one you should be able to figure out.