Is it possible to move a wireless computer between two bikes?
It depends on the bike computer. 

Some computers have this feature, others don't. A brief look at the manual of this computer says yours only supports one bike and you'll need to get another computer for the other bike (or recalibrate it each time you swap them). 
If the tire sizes are the same, you might be able to get by by just swapping the computer between two sensors of the same type, but there may be enough sensor variation that the results may be off by a measurable amount, so I wouldn't recommend that. If the tire sizes are different, you'll obviously need to either recalibrate or have the computer have settings for 2 bikes since the circumferences are different. 

In any case, you need 2 sensors, and if you're using a cheap bike computer, the cost of the other sensor will be close to getting it with another of the same bike computer.