Hello,
I am building a security system for my hives: an Arduino Nano + a gprs module (SIM800L) + a GPS module (NEO 6M). Using SIM cards from Things Mobile, data transmission is very cheap.

Now I need a motion sensor, so that when someone moves the hive, the system sends the coordinates to a web. What could I use?

 

There are a lot of options. The sensor has to account for other movements like wind, bees buzzing inside, etc. Why not use the GPS module to periodically check/send the coordinates, that way you will avoid the interferences and the need of a motion sensor?

 

Instead of a motion sensor, put a switch that operates when the hive is lifted up. Once triggered, the Arduino keeps running to send tracking info.
Have the Arduino in sleep mode to conserve the battery, but every so often, when it wakes, check the battery so it can send a message when the battery is getting low.
To reset it, put a hidden reed switch somewhere so a magnet can be placed against it to put it back in sleep.