It is a frequent opening to a letter to a friend or family member that you don't see often. Concern for the other's well-being shows compassion and interest in their lives.

Thank you. If I use it in a formal letter, for example in a letter to a professor with whom I have been in contact, is it a suitable phrase? or I should use something else?

If you have met them several times and have a close acquaintanceship., it is OK to write in a familiar tone. If you don't know them well, I would keep the tone on a business-like and professional level, not a personal one.

I have been in contact with him through email. However, I have not been in touch with him for about two months. So I think I'd better keep the tone formal, as you said. In this case, is there any suitable phrase I can use instead?

Just introduce your letter with your purpose for writing. You can open by summarizing your prior correspondence:

Dear Professor Kingston;
A couple of months ago, we corresponded regarding your research project on the internal navigational systems of dung beetles. I had the idea that we could further the research by comparing results of the experiments on dung beetles from geographical

I see. Thank you so much