You don't need a school to convert your FAA certificate.
Your first step is getting your Cat 1 medical. That alone can take up to Six month, as unlike with the FAA, the CAME (doctor) has to submit your initial application for a CAMO (equivalent of FAA surgeon) approval.
After you get that done, you to need to write your FAACA (and FAAIA if you want your instrument converted). After that, you fill the application, pay the many fees, submit your FAA certificate for verification (TC will do it directly with the FAA), along with your logbook.
If you also convert your instrument rating, you will need an IPC signed by a CFII from the previous 24 months (your DPE can also sign it, if it's from the last 24 months). If you want to get a group 1 IFR, you will need an FAA CMEL, otherwise a CSEL will be converted to a group 3.
When you're done - you will need to get a radio operator from Industry Canada, and very recommended to get your ICAO language test done (the FAA certificate has a built in level 5 proficiency good for 4 years).
Being there, than that. Good luck!