This will entirely depend on the nature of the appreciation and is also a question of tone. When writing fan mail, remember to bear in mind several crucial points. When you are writing to someone you know to say, for example, how much you enjoyed reading their book, think about how well you know that person and whether they are likely to be surprised or embarrassed by your letter. If this is case, make sure that your letter is not too personal. Appreciation without cringe worthiness probably the tone to aim to aim for
When writing to a complete stranger, possibly a celebrity, to say how much you enjoyed their role in a film, for example, bear in mind that your letter will almost certainly go through the hands of four or five may be people before it gets to the recipient, if ever.
try to avoid sounding too intimate since this would clearly be inappropriate. Again, sincerity is the key, although, o this occasion, sincerity should be tempered with articulate and positive criticism. Just bear in mind that, although you may know this persons work by heart; you are a complete stranger to them.
They may be excited to get fan mail, but they won’t be if they think it’s from a weirdo.
As a general rule, the more specific you can be about why you like this person’s work, the better. Try to concentrate on what you like about that work itself, and not get confused with the person who wrote the book or acted in the film. Think about why you want to write to them.