You cannot. The Guitar Hero III (Les Paul) wireless guitar uses a different proprietary 2.4 GHz protocol than the Guitar Hero II (Gibson X‑Plorer) wireless guitar. The PS2 dongles are not cross‑compatible.
Bottom Line: For authentic PS2 GH2 play, source the correct Gibson X‑Plorer (wired or wireless). The Les Paul is physically incompatible with the GH2 dongle.