It's an odd sentence, certainly. It's technically grammatical, but there's no good reason to phrase it that way. Much of the point of using the passive voice is to avoid identifying who's acting. You don't often use the passive voice and then go ahead and identify the acting party anyway.
For example: "The teacher has been sent the project."
This is the normal use of passive voice. The speaker either doesn't know who sent it in, is trying to conceal that information, or just doesn't think it's relevant to the discussion. Passive voice puts the emphasis on the action or the recipient, depending on how it's phrased and what you do with it.
That's why passive voice is so popular for companies making non-apologies. "Mistakes were made" doesn't specify by whom; it spreads out responsibility across the entire company, so it's nobody's fault. "A mechanic and his supervisor made mistakes" assigns blame to specific people (or at least roles).
To me, the sentence you provided feels indecisive -- it's as if the speaker started out trying to avoid blame for something by dropping into passive voice, then halfway through realized it wasn't being received well, and tried to fix it by saying who did it after all.
That said, there are times when you would do something like this for a specific effect. For example, "The car was driven by my father" is totally valid. In this case, you're not trying to conceal your father's involvement, but rather you're emphasizing the act of driving over the person doing it.
In that sense, you might write something like "The report was sent to the teacher by the students" and it wouldn't be strange, but "The report was sent to the teacher by us" does have an odd, awkward feel to it.
I'm not totally sure why "us" doesn't feel right in that phrase while "the students" does; I suspect the problem is that using passive voice about something you yourself did always reads like you're trying to conceal or deflect responsibility for the act, so then admitting to it later in the sentence feels like a reversal of intent.