At the moment, however, bitcoin is in its early stages, and it can't solve the problem.
Because bitcoin transfers are slow and I think very few people are willing to pay for a transaction.
Actually there are many altcoins that are faster and have cheaper transaction fees than bitcoin. But yes, cryptocurrencies are still young and arent being mass adopted yet.
However, its true that cryptocurrencies will kill fake money for sure. There is no way you will be able to fake bitcoin except you can hack it which is very very difficult.