[I was wondering where the term theanthropos was used first and by whom?
Maybe you can help me?]
The term literally means 'God Man' and was probably used when the Nestorian controversary was being address since it refers to the two natures of Christ.
3. Ephesus - The Victory over NestorianismAlexandria's second major success was won by the nephew and successor of Theophilus, St Cyril of Alexandria (died 444), who brought about the fall of another Bishop of Constantinople, Nestorius, at the third General Council, held in Ephesus (431). But at Ephesus there was more at stake than the rivalry of two great sees. Doctrinal issues, quiescent since 381, once more emerged, centring now not on the Trinity but on the Person of Christ. Cyril and Nestorius agreed that Christ was fully God, one of the Trinity, but they diverged in their descriptions of His humanity and in their method of explaining the union of the divine and the human in a single person. They represented different traditions or schools of theology. Nestorius, brought up in the school of Antioch, upheld the integrity of Christ's humanity, but distinguished so emphatically between the humanity and the Godhead that he seemed in danger of ending, not with one person, but with two persons coexisting in the same body. Cyril, the protagonist of the opposite tradition of Alexandria, started from the unity of Christ's person rather than the diversity of His humanity and Godhead, but spoke about Christ's humanity less vividly than the Antiochenes. Either approach, if pressed too far, could lead to heresy, but the Church had need of both in order to form a balanced picture of the whole Christ. It was a tragedy for Christendom that the two schools, instead of balancing one another, entered into conflict.
Hope this addresses your question.