Yes, you are to file a Quebec return as this was your end of December address. When you answer the questions in the beginning interview, the software asks where you live on December 31, 2023 then the next question asks if you "Did you move from another province/territory in 2023?" On each T4 you will enter, you will be entering the province you worked in for that employment. Unfortunately, TurboTax software does not support multijurisdictional returns.
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