You are visiting an office, and read: "I'll be back in five minutes." What have you been informed? Not that the person will return five minutes from now. Nor that the person will return five minutes from having written the note, since such notes can be re-used (this nicely shows that one can make an extended utterance simply by tacking up a sign—one is uttering, without writing, speaking or gesturing). Rather, you've been informed that the person returns five minutes from when the sign was made public.
You, obviously, understand the sign, and know what it says. What the sign says is, of course, the proposition which it expresses. So what does the sign say to you? It tells you, informs you, that the person returns five minutes from then, where of course the demonstrative "then" points to the time at which the sign was published. But that the person returns five minutes from then is a B-proposition. Hence, what the sign tells you is a B-proposition.
But unless we want to special-case posted signs, by exactly the same token when a person leaving an office tells you "I'll be back in five minutes", she is apprising you of a B-proposition, namely that she returns five minutes from then. It is simpler to handle the sign case and utterance case uniformly, so let's do that.
So now we see that paradigmatic A-sentences express B-propositions. But the A-theorist thinks that A-sentences express something other than B-propositions. Hence the A-theorist is wrong.
Objection: What you learn from the sign is the A-proposition that the person will be back five minutes from then.
Response: That is incorrect. Suppose that the sign was published at 1:30 pm, and you're reading the sign at 1:40 pm. The sign is informing you that the person is back five minutes from then, i.e., from 1:30 pm. But it is ungrammatical to say that you are informed that she will be back at t, when in fact t is in the past. (This is an interesting case of the phenomenon that whether a sentence is grammatically correct depends on non-linguistic facts. Another case would be the use of non-generic gendered pronouns.) Grammatically, what you would need to say is that she was back five minutes from then. But you can't say that if you don't know that the sign was published more than five minutes ago. So if you want to stick to tensed language, what you need to say is that she (in the generic sense of "she") was, is or will be back five minutes from then. That is, indeed, an A-sentence, but an eternal one. If all A-sentences express eternal A-propositions, then the the non-eternality in the A-theory is lost, and one might as well be a B-theorist.