Is Guitar Hero II Compatible with Guitar Hero III?

No cross-compatibility.

• Guitar Hero II (PS2, Xbox 360) uses a proprietary dongle/wired connector specific to its guitar models (X-Plorer, Gibson SG).
• Guitar Hero III (PS2, PS3, Wii, Xbox 360, PC) introduced a new wireless protocol (Les Paul controller) and different dongle IDs.

You cannot plug a GH2 guitar into a GH3 dongle (or vice versa) and have it work. Each game requires its own matching controller hardware.