As a rule, as soon as an employee informs his employer that he is leaving how should the company act? First of all they should discover the reason why the employee had resigned, whether there are any unsatisfactory conditions of working, problems in the team or anything that could be improved. Secondly the company should go in for internal promotion and establish whether there are any candidates to be promoted to the vacant position.
If there are no internal candidates to be promoted the company should advertise the vacancy or turn to a recruitment agency. The next step would be examination of the applications, resumes and covering letters as well as combination of short-lists of preliminary selected candidates.