There's no magic about this. If he writes a second letter in order to avoid an extension, then he's frustrating the Act and it's unlawful. If he writes a second letter for some other purpose (and with some other effect), then it's not. But that prompts the question: why bother?
I think a letter on the boundary would say: "I accept my obligation to seek an extension, and I am seeking one. Let me tell you what I intend to do with it: I will not negotiate further, and the UK may have a lower appetite for consensus in Council, given its trajectory."
I think that if the letter said
"it is not the policy of the UK gvt that Article 50 should be extended", or
"the gvt hopes that the EU will reject this request", or
"an extension would not be in the interests of either party for these reasons"
... then it would be unlawful.
"it is not the policy of the UK gvt that Article 50 should be extended", or
"the gvt hopes that the EU will reject this request", or
"an extension would not be in the interests of either party for these reasons"
... then it would be unlawful.
