Hi,
I have a question about the proof. Do we have to provide the Government ID that has same address on it ?
or would it be possible to submit the explanation letter instead ?
Your question is too broad with too few specifics to say.
Government ID helps support your case - significantly - but in itself may not be enough. You can provide a letter of explanation, but it would be unusual for a letter of explanation alone - without additional supporting documentation, government, private, whatever - to be sufficient.
Put differently: for common law, they will look at the balance of evidence. For a couple with long time residing together and children (for example), the lack of any single document is not likely to cause a problem; for a couple barely over twelve months residing together, the balance of what is required will be much higher. (Also may depend on country context, inside Canada or outside, etc.