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We are thinking for about a month that she will stay there in home country and then come back after a month. Do you think if that works?

Only CBSA will determine whether it will be an issue. In general a month out of the country is not a lot after a long stay. A supervisa does not allow someone to permanently move to Canada. A one month visit appears that you are only visiting your home country. Given the fact that there was a significant overstay I would personally consider staying out of Canada longer but there is no way to know whether your mother will be denied entry, given a limited stay in Canada or have no issues.
 
Only CBSA will determine whether it will be an issue. In general a month out of the country is not a lot after a long stay. A supervisa does not allow someone to permanently move to Canada. A one month visit appears that you are only visiting your home country. Given the fact that there was a significant overstay I would personally consider staying out of Canada longer but there is no way to know whether your mother will be denied entry, given a limited stay in Canada or have no issues.
thanks for the reply, I will update here on what happens with our case.
 
is there any news or update about this situtation? because my grandmother has the same situation and she overstayed for at least 7 months. we just knew because we were just about to extend her stay that we thought it's 2 years.

Just an update about my grandmother's situation. She went home in 2018 before any removal order from Canada.

2019: we submit our interest to sponsor form.
2020: interest to sponsor form was accepted
2021: stated the sponsor application
10-2023: She visited Canada again with eTA while her sponsorship application is in process
12-2023: She was approved to be a Permanent Resident in Canada.