I'm sure you're worried that you won't be able to prove you are still common-law partners if you don't have the same address when you submit the application. So you have a couple of options:
In Section 5.36 of the
OP2 Processing Manual, they talk about common-law qualification when the partners are not currently cohabitating.
How can someone in Canada sponsor a common-law partner from outside Canada when the definition says “is cohabiting”?
"According to case law, the definition of common-law partner should be read as “an individual who is (ordinarily) cohabiting”. 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 (see also 5.44 for information on persecution and penal control). 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."
So, you have a couple of different places on the application where you need to put addresses. One is in the sponsorship forms that your sponsor is filling out. He should put the address where he will be over the next couple of months, because that's where he'll likely be when they send his notification letter for approval to be a sponsor. (Remember, if he is ordinarily living outside of Canada, he needs to include evidence with the application of his intention to return to Canada when your PR is approved - so having to attend training in Canada as part of his job [or whatever it is] might speak to his intent to eventually resettle in Canada, and could actually work to your advantage.) As far as your address - there is a requirement for a mailing address and a residential address. The residential address is where you are currently living - either in your country of birth, or a country where you were admitted with temporary status valid for at least one year. Your mailing address might be the same, or it can be different - but the mailing address will be wherever you want Immigration Canada to send correspondence to you about the process.
If your addresses have to be different right now, be sure you include a letter - signed by both of you - indicating how long you anticipate being separated, and why. They may ask you later on in the process to show that you are living together again, so don't be afraid to be honest about how long it will be before you're "co-habitating" again. Remember, periods of separation are permissible, as long as the intent is to resume the relationship as soon as possible.
Your other option would be just to wait until you're back together again, and then submit the application when you have the same address - but you probably don't want to wait for months to get this started and, according to the manual, you don't have to. I'd just use your new addresses and submit the ap as soon as you know you can have access to those addresses for receipt of anything they might send to you. Your partner won't hear anything about sponsorship approval for at least 35 days - but, if the ap isn't complete in some way, they will send it back pretty soon after receipt. You won't be hearing anything from the overseas visa office for at least a couple of months.
Once he's back with you again, and you resume your cohabitation, update the embassy with that information and any new address.