Which one is a correct one:

With this letter I intend to...


With this letter, I intend to...


For short prepositional phrases at the beginning of a sentence, the comma is optional.

See Purdue OWL

This website says to use a comma after a long prepositional phrase, and not to use a comma after a short prepositional phrase, where they define short as "fewer than five words".

Having an exact cutoff is overly prescriptive, most English writers don't actually count words for this, they just go by feel. There's absolutely nothing wrong with putting in a comma after a three-word prepositional phrase, or leaving a comma out after a simple five- or six-word phrase, if you think this sounds better.

So both options are grammatical in your sentence. Use whichever you think sounds better.

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