Moscow is considered the third Rome(by russians), Russia considers itself as the continuation of the Byzantine Empire and the protector of Christianity(orthodox). Hence all their wars against the Ottoman Empire/Turkey, their support for the creation of a greek state, etc.
Some Byzantine Emperors were from Albania(Illyria).
Some Emperors had serbian mothers and the daughter of the last Byzantine Emperor married a serbian ruler.
But in the end, we all know who is the real successor