He applied for his PGWP in May, almost 4 months ago. Now he has a job offer and the last 3 paychecks (from april), he will work in the same job that he was working when he finished his course. Now he is not working because he cannot, as he applied for PGWP on implied status (at that time he was waiting for his extension of Study permit). If I have to wait to receive his PGWP, my OP will expire. So, I am really concerned and I don't know if I should apply for my extension of OP with a letter of explanations. Thank you for your response.
Seems like you are in a very unfortunate situation. At this point your best option seems like waiting for the approval of your spouse's PGWP. It might take until late-November/early December to get his PGWP, and will require you to first apply for and get a visitor record, and then apply for and get approved for a SOWP, which might take until next summer, who knows. If I was in your situation, I would do what you suggested, ie, really emphasize in the letter of explanation that your husband will continue to work full time in the same position he was employed in part time while he was a student (assuming it's NOC 0, A or B) and provide them with the offer letter along with paychecks from his past employment as a student. Also mention that you will submit a copy of your husbands PGWP and 3 paystubs after he begins work, and the only reason you don't have that in hand is due to COVID-19 related disruptions. There will be a time window between your husband receiving his PGWP, working for a few pay periods, and your work permit application to begin processing, and the time window will be quite big given that you will be submitting your application a lot later. Submit your husband's PGWP and the paychecks through the CIC Webform during that time. Officers are humans, they understand that COVID-19 related disruptions messed everything up for a lot of people, and when the officer has all they need to establish your eligibility when processing your application, I like to think that they would decide in your favor. Good luck!