What's what here? I'm going to disagree with Allan Pollack and analyze the structure as follows:
A - "As I write this letter" etc.
B1 - "Treasure these few words" etc.
B2 - "I'll be coming home" etc.
A' - "As I write this letter" etc. with slightly different chord progression
B1 - see above
A' - see above
B2 - see above (with added coda)
I have a tendency to think that A and B work together as two parts of a chorus. The B2 section seems to suggest otherwise, though, as the idea of a chorus with two parts where the second part is then repeated with new words feels like we are stretching the definition.
Can the B section really be considered a verse, though? It consists of only a single pair of rhyming lines and then the refrain of the title words. ("Refrain" tends to imply chorus or at least some suggestion of chorus to my thinking.)
The A section is certainly not a verse. It has the same words in each of its three utterances. Even though it ends with a perfect authentic cadence, it doesn't feel complete enough to be a chorus in and of itself. It's only eight bars long and consists of four lines of text with one rhyme (lines two and four).
Every time it's heard, it's followed by the B section (either B1 or B2). If B is indeed the second part of the chorus, then we are looking at a song here that is, in fact, all chorus.