Modern American English: "Please advise that..."

[Kazuaki Shimazaki II]

Consider this paragraph from my boss, a native speaker of American English (names blanked):

Dear <X>
Please advise that <Name> has already sent <my> chair to <you>. Kindly ensure to load the chair last, and do not stack with heavy cartons. We appreciate that you will instruct your warehouse colleague to include the chair in the container and handle it with care. Kindly confirm"

Going straight with the definitions, "Please advise that" is active voice, and in the sentence, the 'subject' is implied to be X, but the 'object' or 'target' (who this advisory is directed to) is not even implied. Thus the sentence is logically invalid, let alone its grammatical syntax (to be frank, the finer points of theoretical English grammar is not my strength).
Thus, I thought, based on the context, that she meant to say:

Dear <X>
Please be advised that <Name> has already ...

At least it'll seem logical considering the content of the rest of the paragraph.
My boss, however, said that this is modern American English for (that is, she meant to say):

"Dear <X>
Please advise whether <Name> has already sent <my> chair to you..."

She said that "whether" is too "troublesome"...
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I must admit. I think my English is pretty good, near or at native level, and had it verified by getting a 8 in IELTS (of course, tests are not too representative, but one has to start somewhere, and I never had any trouble talking to English-speakers).

But using "that" as a substitute for "whether" is a new one on me.

Of course, the boss is always right, language evolves in strange ways, and searching on the Internet, Google did reveal 7,200 hits with "please advise that" so at least it isn't completely unused, but this seems to go against the normal usages of "that" so much that it is hard to believe.

So I'm curious to know what's the "status" of this expression in American English.

Is it grammatically proper?

Or is it improper but common, even in formal situations? Sometimes common usage is more important than being true to theoretical grammar...

Or is it suitable only for colloquial situations, or uncommon but not unknown - or just a full blown error?

Just for personal knowledge. Thanks in advance.