This is a necessary condition, and everyone needs to sign. It would be nice if there was an invitation or something. If it really doesn't work, just copy the signature of the invitation, and then it will look more like it (just a copy of the inviter's passport or identity certificate). As long as the signature is not too bad and other materials are complete, there should be no problem. This is only a last resort. It is best to urge the Italian side to send a fax or a copy.

Note: Their identification will be fine. I used to have an avatar with numbers and signatures written next to it.