"believe me to be"? What is it?

I’d like to ask about the sentence in The Final Problem by Conan Doyle.

Pray give my greetings to Mrs. Watson, and believe me to be, my dear
fellow,

This is supposed to be the last message written by Sherlock Holmes to Watson.
I haven’t learned and don’t think ever saw the wording like the underlined part before. What’s this?
I think since it’s a farewell message, it has to mean something like “I’m always with you in your heart” or “Pray think I was alive”. I don’t know.
Would someone paraphrase this part to me please? Thank you.