FYI I am currently in BC. I think that I had this bike registered here before Alberta and am going through an established government mechanism to find out. But I am completely clueless about Alberta. 

Quebec  2021 . I believe it is impossible to register an undocumented bike  in Quebec . I have  spent many hours trying to register a basket case with no papers . The "Sell it to your mate in Ontario and he will register it on a Bill of sale and then sell it back to you with an Ontario registration " plan will not work .It's an attempt to stop chop shops welding the front end of a stolen car  to the back end of another stolen car to create a new undocumented car   -or something - the explanation got too convoluted for my level of French .

You can go the " artisinal fabrication " route where you assemble a bike from parts and attempt to register if via an ill defined process dictated by the SAAQ .You risk rejection after spending time and money . At best the rebuilt  bike would be registered as a  " Muppet 650 Mark1 Artisinal" , which would have a lower value than a rebuilt Bonneville .

I suspect that there are barns all over Quebec stacked with bikes which are only saleable for parts or scrap 

nvoluted.Old bikes are cilateral damage  for my French 

What year did you register the undocumented Suzuki on a Bill of Sale??

In 2020 Montreal cops , 3 SAAQ outlets , and a  guy in SAAQ head office in Quebec City all said' no way '

At present the only option seems to be building it up from parts,attempting to register it as an " Artisinal  Build "and submit it forSAAQ verification . You might get a registration for a "2021 Artisinal built Muppet MK1 650" rather than a 1970 Triumph Bonneville .

Or you might spend time and money on a project that is rejected by the SAAQ with no explanation 

inspection 

Quebec sait  faire , A story mind games with the SAAQ and Revenu Quebec in 2021 !

I have been all round the SAAQ bureaucracy trying to register an old bike .

 Here are my conclusions 

SAAQ does not want to know about old bikes 

No paper work ? Forget it it, is impossible to register a bike, with no paper work in Quebec .

You could try the "Artisnial Fabrication "route , where you build a bike from parts and try to register it . At best your lovingly rebuilt Bonneville might eventually  be registered as a Muppet Mark 1, or it might get lost in the quagmire which is the SAAQ . It would a major crapshoot where the SAAQ will probably win .

Even with paper work it is an uphill battle to register an out of province bike in Quebec .

 I bought a 1972 Triumph Tiger in Ontario , with Ontario registration papers  I also  established from the Revenue Quebec web site that the value for Quebec Sales Tax  was " Generally " assessed on the price on the Bill of Sale for transactions between private parties. No separate evaluation was required in this particular case 

The SAAQ clerk didn't even  want to see a Bill of Sale , she demanded an " Evaluation from a Quebec Source" and was hostile to the " import  of a Foreign Bike" . Her attitude was supported by her manager  .

Revenue Quebec agreed with the SAAQ , despite the contrary  statement  on their own website ! Apparently ' generally " has a different meaning in Quebec government speak . Revenu Quebec can do whatever they want .

I appealed this interpretation and also set my MNA loose on Revenue Quebec . Result ? I needed an evaluation to register the change of ownership !!! I now have an evaluation an a Quebec registration .

Given the loosy goosey wording of the Artisinal Fabrication documentation and the creative use of  language by the Quebec government , I'm glad I decided not to venture down this road !  

Quebec