By the fact that a Church Council reinstated him to the see.
I am getting two different stories, here. Your article claims that the Rome endorsed the Council of Constantinople (879-880) as ecumenical. However the article I read put out by Rome is that although the legates allowed the will of the Photian party, which was the majority at the Council, to prevail Pope John VIII condemned the council altogether.
Legates can only represent the Patriarchate at a council. Once the council has been dismissed the Bishop of the Patriarchate must give his stamp of approval. This Council only served to resurrected the schism of Photius/Nicholas and Pope John VIII excommunicated St. Photius on spot.
So how is it that your article claims that Rome endorsed the Council of Constantinople (879 -880) as ecumenical when immediately coming to knowledge of what transpired Pope John VIII excommunicated Photius?
Furthermore Photius was ordained a little too quickly, however that's not that big of a deal. The main two issues for me is how a person can be ordained by someone who was excommunicated? Then there's the simple fact that Ignatius was never deposed from his position in Constantinople anyway. Since when does a secular emperor have ecclesiastical authority to depose of a Patriarch.
I understand the See was physically void of its leader because Ignatius was banished but that has never been a cause that annulled the reign of a Patriarch. St. Ignatius of Antioch didn't stop being the Bishop of Antioch while bound in chains on the road to martyrdom. How is that Photius even thought that he could assume the role of an already filled Patriarchate?
I understand that after Ignatius died, Photius was the popular vote. Rome respected the right of the clergy to elect their own Patriarch and endorsed Photius. The question I have is what's with the mess before this?