我从http://www.afe.gouv.qc.ca/ 下载的文件上获知申请条件:“You have been residing in Québec for at least three months and have not resided in another Canadian province for more than three months.”
you can apply for L&B after you arrived in Montreal three months. you cannot act as BC resident. you can prove your passport and air ticket to show that you are not living in outside of Quebec more than 3 Months.
Good luck
As I knew, some friends of mine could not be treated as a quebec resident like you even though you just stay in Vancouver for a while and you will stay in montreal for three months.
"have not resided in another Canadian province for more than three months" does mean your staying out of Quebec would be same sense for them. Good luck.