CICのマニュアルに
How can someone in Canada sponsor a common-law partner from outside Canada when the definition says “is cohabiting”?
という項目があります。
According to case law, the definition of common-law partner should be read as “an individual who is (ordinarily) ohabiting”. After the one year period of cohabitation has been established, the partners may live apart for periods of time without legally breaking the cohabitation. For example, a couple may have been separated due to armed conflict, illness of a family member, or for employment or education-related reasons, and therefore do not cohabit at present. Despite the break in cohabitation, a commonlaw relationship exists if the couple has cohabited continuously in a conjugal relationship in the past for at least one year and intend to do so again as soon as possible. There should be evidence demonstrating that both parties are continuing the relationship, such as visits,
correspondence, and telephone calls.
This situation is similar to a marriage where the parties are temporarily separated or not cohabiting for a variety of reasons, but still considers themselves to be married and living in a conjugal relationship with their spouse with the intention of living together as soon as possible.
For common-law relationships (and marriage), the longer the period of separation without any cohabitation, the more difficult it is to establish that the common-law relationship (or marriage) still exists.
というわけです。
日本とカナダに分かれていてCohabitationの状態ではないけれども、Conjugal Relationshipが続いている、つまり①離れていてもお互いが事実婚の関係にあるという共通の認識を持っていて、②連絡を取り合い、③可能になり次第また同居することを目的としているというようなことが*客観的に*証明できればCommon-Law Partnerであると認められるでしょう。
もっと詳しくはこれをじっくり読んで研究してください。
http://www.cic.gc.ca/english/resources/manuals/op/op02e.pdf
トピ主さんたちは今でもジョイントアカウントがあるということですし、国際電話の記録やメールのやり取りなどで証明は可能だと思います。ただ、ジョイントアカウントがあっても、ステートメントに名前が載っているだけではなく、実際に彼がトピ主さんの国際電話代を払っているとか、トピ主さんも給料の一部をジョイントアカウントに定期的に入金しているとか(その逆も)そういう事実がないと難しいかもしれませんね。