In the opening paragraph, thank the recipient for considering you for the position and sending a job offer. A sample letter offering a job contingent upon the results of a background check or other criteria.When accepting a job offer, let the company know you are grateful they took time out of their busy schedule to offer you a job. Be prompt in your response. When you accept a job offer letter, it's OK to ask for a couple of days to think about it. Letter for Social Security Number Application Form. Then enter the name and address of the potential employee who is being offered the position. Next, after Dear enter the name of the potential employee.