This in an interesting assignment designed to help students understand the presuppositions they bring to reading Hamlet. There is no right or wrong answer here. It is an assignment simply designed to help you think through your attitudes towards a mother's remarriage.
As you work on your response, the first thing you should think about is the rhetoric of the letter. Both the letter and the description of the situation focus entirely on business issue, yet most marriages are about personal relationships as well. This is not just a story about hiring a business manager but one about a deeply personal choice. The first paragraph of the response letter might want to address sympathy for the mother's grief and whether you think this choice will ultimately make her happy. It would be appropriate to ask whether outside of the business issues she thinks that this is a good life choice and express sympathy for her in this difficult situation.
Another issue to address is whether one can tell if a business is flourishing in such a short period. Usually, it takes a few quarterly reports before one would make such an assessment. Thus, it might be prudent to suggest that while you are happy for her, it might be a good idea to wait a few months before making such an important decision and let you graduate from college and return to participate in the business first.
Further Reading