Is it permissible for a Muslim to leave his Christian colleague to complete his work after official working hours on Friday, and is this considered an encouragement not to cease buying and selling on Friday, and should he pay him for his assistance?

There is no blame on the questioner for leaving unfinished tasks for his Christian colleague to complete on his behalf. This does not constitute an encroachment on the sanctity of trade during Friday prayer, because his colleague is not Muslim, nor is he in an Islamic society. He is not obligated to pay him compensation as long as he is volunteering to do so, and it is permissible to seek assistance from a non-Muslim in matters other than acts of worship. Nevertheless, it is better to give him compensation so that he does not have a favor over him, based on the hadith: "Do not ask people for anything." We also point out that the permissibility of traveling to disbelieving lands is conditional on being safe from temptation and being able to establish religious rituals.