Controlling IR LED strip with Arduino.

Hi.

I brought this LED strip for lightning project and I wondered if it is possible to take the LED driver box apart, hook it up to my arduino and control it directly?

The box has this 3 wire IR-receiver, which receives IR messages from the remote and sends them to controller. I know that I just could hookup an IR led to my Arduino and control it that way, but I wondered that I maybe could cut the wire to IR-receiver, solder some longer wires to them and plug it directly into my Arduino.

Is this possible?

Yes, that is probably possible.
If you want to simulate the IR code, you better replace the IR led with an optocoupler. That keeps everything nicely seperated, and the electronics of the LED strip might not even notice that it is an optocoupler.