Your open collector style sensors need +5V and ground (0V) connections,, then the output signal switches to ground.
The interface board has inputs that need switching to +5V, not ground.
If you want to trigger when the sensor turns on, you will need to add a PNP transistor and some resistors, or a P channel logic level FET and a single resistor to each input, to adapt the signals.
Or, if you want to trigger when the sensor turns off (when the beam is broken?), connect 5V power and ground, then connect the sensor output to the inner pin on the button input connector; the outer pin is +5V.
Also add a resistor between the two pins on the input connector so it will trigger the input when the sensor turns off.
Try 1K to start with, if that is at all erratic try 470 Ohms. From the IR sensor data, you could go down as low as 100 Ohms without risk of damage, but I'd try higher values to start with.
I found an article with a lot of info about that interface here, it shows how power is routed aroudn the connector pins and which are 5V vs input signals; look for teh image of the board with the red highlighted track.
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