Hence, we can conclude that this mod requires only an online profile. But I only use a local network with an offline profile.
(no options )

Then tell me, what version of the game do you have?
And I mean a local area network without Internet access. Does this option work for anyone?

Thank you for your answer, but alas.
Of course I use LanFix.
As soon as I apply the file d3d9.dll (r45), then in the boot menu of the co-op game over the local network, I get the message:
"Server authorization error, please try again."
The version of my game (CD "R...

I have a CD version, I tried all possible options with the T4M(r45)  mod to play on the local network. USELESS! It doesn't work on LAN at all.
 

this does not work in a multiplayer game, only single player (firebox)