First of all I was lack of some tool - it is a sniffer! I have googled and downloaded the first one that was free. It appeared to be "IP Sniffer". You can find it here:
Erwan's Lab or use any other you love. On launch you see the main window where top left part is table of IP frames, bottom left is frame viewer and right one is header info.
First select correct IP of the interface corresponding to your Internet access. In my case it is private IP, so I don't need to paint it over - envy me guys

(yeah, I've just found the advantage of private IP)!
Now let's learn IP address for the site that produced the problem. It was... well, I think you know it yourself.

It can be done with a lot of ways. I'll do it in IP Sniffer.
Tools => DNS => Local Resolver and you are ready to input site address.
Now we know IP and can filter IP frames by IP destination. Click "Filters" button (right to your IP address) and fill the field "IP Destination" with site IP. Can't do it? Use "+"!
Click "OK" and run listening by pressing "Start" button. Now return to the browser and refresh the page approving resending data. Alttab back to sniffer and stop process. Now feel yourself a hacker

and begin looking for frames with useful data, top to bottom. When found select (see screenshot) and copy it with
Edit => Copy selection (text).
Paste it in your favorite text editor. There can be some trash symbols in the end - delete them. If your epistle was as much as my one you'll have to repeat operations with several next frames concatenating text in editor.
Your experienced hacker's eye of course noted that something is wrong with text! Yeah, after sniffing a real hacker must decrypt data! I'll help you! Try some replaces like:
'+' => ' '
'%2C' => ','
'%28' => '('
'%29' => ')'
':' => '.'
'%3Cbr%3E' => '\n' (line breaks should be replaced in Esc-sequences mode)
... and so on.
After that text must look nice. It is done!
Message to you
I am not sure this "tutorial" can really be useful, but I hope I made you smile.
Just for fun, guys!