With an FAA liscense you can only fly N-registered airplanes, so if their airplane has a C tail number, that'll be somethig to look into as well. The conversion to Canadian liscense is fairly simple from what I have heard.
§ 91.711 Special rules for foreign civil aircraft.
(a)
General. In addition to the other applicable regulations of this part, each person operating a foreign civil aircraft within the United States shall comply with this section.
(b)
VFR. No person may conduct VFR operations which require two-way radio communications under this part unless at least one crewmember of that aircraft is able to conduct two-way radio communications in the English language and is on duty during that operation.
(c)
IFR. No person may operate a foreign civil aircraft under IFR unless—
(1) That aircraft is equipped with—
(i) Radio equipment allowing two-way radio communication with ATC when it is operated in controlled airspace; and
(ii) Navigation equipment suitable for the route to be flown.
(2) Each person piloting the aircraft—
(i) Holds a current United States instrument rating or is authorized by his foreign airman certificate to pilot under IFR; and
(ii) Is thoroughly familiar with the United States en route, holding, and letdown procedures; and
(3) At least one crewmember of that aircraft is able to conduct two-way radiotelephone communications in the English language and that crewmember is on duty while the aircraft is approaching, operating within, or leaving the United States.
Looks like it's no problem, just can't operate it in Canada unless I get my certs Canadianized (that's a good idea?)