Help with a double board setup

Thank you for the tip ! I can think about the wireless later on but the most important question
for my project is how can I make a board become like a mirror to the other one ?
Not really implementing a master/slave mode but having both boards react the same and together,

Board 1 & 2 with the same layout ( one button and one LED )
When I press the button on either board one or two, both leds will light up. Is this possible ?