Replace one of the 3way switch to sensor switch in the hallway
After wrestling with 3way (i call them "two pole" but to each their own) switches I have learned that the only way out is patience and testing.  Don't trust the wire colors.  Unhook the switches from both sides (or just one switch if you are sure the other hasn't been altered since it was working), put wire nuts on the open wires, and power the circuit back on from the breaker/fuse.  Get a multimeter and look for where the hot/neutral is and try to work out the other wires (which ones run to the fixture and which run to the other switch).  If it's not obvious yet, check the fixture for voltage, you might find voltage there even with the switch off (second scenario below).

There are two types of 3 way switch wiring layouts.  One has the power running from the panel to switch A, then 3 wires running to switch B (two alternating hot depending on switch position, plus one neutral) and finally 2 wires running from switch B to the fixture.   The other option is similar but power runs to the fixture first and then to the switches to make/break the path.  

You need to know which of these applies to you in order to know which terminals on your motion switch to use.  From the look of the switch you have the black (live) wires hooked in but it's not clear if there is a neutral in there too (most motion switches need a neutral to work in a 3way setup).  More details will be needed on your situation to provide a specific answer.

Edit, more info:
Came across this good discussion (in case you haven't seen it): How do I wire a 3-way motion sensor?

The crux of the problem is that in a normal 3-way switch set up, neither switch really "knows" if the light is on or off, flipping it just reverses the state (for example you can have two switches up and the light is still off) so with a motion sensor you really need it to be in total control of the light, otherwise it might just turn it off after sensing motion when the light is already on per the other switch (not what you want).  Most motion sensing switches have an accommodation for this but it is specific to the model.