Yes, it is true that you can move a phone to another network, but:

1.) You need the unlock code for the specific model/original carrier combination. This can be obtained through Orange or online through a number of third parties; I cannot recommend one in particular, though I should note that there are a lot of fraudulent sites/services out there, so be careful.

2.) Unlocking your phone without the original carrier's authorization is not legal in all areas; consult you city/state/federal laws before proceeding.

3.) Your new carrier (O2) must not prohibit the phone on its network (rarely an issue) and must support the phone's technology (CDMA vs GSM).

4.) Official carrier support is not required, but they also will not assist you with any phone-related problems such as SMS not working properly, poor signal quality, etc. unless it's a service issue that also affects their own phones.

5.) Carrier-specific features/services, such as a live TV service, may not be available on the phone.

Hope this helps,