Nadya,
There really isn't any way.
Well I guess you could have the printer run it's output into a scanner system, which would OCR each page and compare it to what was supposed to be printed.
Bottom line, between network problems, paper jams, someone tripping over the printer power cord.. there is no absolute way to know that the user got the report into their hands.
>I've searched UT, but was not successful. Here is a simple question: how can we check, if the report was physically printed? If, for instance, we're printing lots of files from some directory, is there a way to see, what was actually printed?