Especially when there is no internet connection.
For this, gossip protocols like Briar are good. Otherwise, the good answer is to build actual networks on site. It's not hard to build a local network and it's not have to find a slow uplink to get some information out, what's hard is to provide decent connectivity to thousands of people on a budget if key infrastructure has been damaged.
Do we have tools that could be useful in the fight against misinformation in Russia?
No tool can help against manipulation/disinformation. The only thing that would come close is reputation/karma systems on internet forums, but that does not enforce a single "truth" across the network, and it's a good thing! If your tools can fight against disinformation from a specific actor, it can also be used to fight against actual information from the people, depending on who controls it...