No, no, no: I'm asking you to clarify! My previous post makes a lot of claims re the Anglican Communion and you're asking how the Communion fits in. The question I suppose I have is "which claim do you want me to justify?" You're effectively asking a number of questions in one.
If you're asking "how does the AC relate to the pre-1054 Undivided Church?", then I would refer to their use of the Apostles' and Nicene Creeds as basic statements of faith, their use of liturgy (the Prayer Books for example have a Penitential Rite, a Liturgy of the Word virtually identical to Catholicism and Orthodoxy, prayers of intercession, and a Liturgy of the Eucharist pretty similar to Catholicism and Orthodoxy complete with Sursum Corda and similar Eucharistic Prayers with just the epiclesis slightly differently worded to reflect the more nuanced version of the Real Presence to which I've earlier referred), threefold ministry of bishops, priests and deacons, etc
If you're asking "how is the AC a valid successor to medieval Catholicism?", then I would refer to the statements about liturgy above and in particular point you to the continuation of the Sarum Missal which is still used today and is a liturgical survivor from the medieval Catholic Church in England and thus arguably more on all fours liturgically with medieval Catholicism than the modern Catholic Church, the preservation of Apostolic Succession with the consecration of ++Matthew Parker in 1559 and accompanying 'branch theory' etc
If you're asking "how is the AC reformed or Reformed?", then I would direct you again to the Prayer Books (in particular 1549, 1552 and 1662), the 39 Articles of Religion of 1563 and direct you to the websites of contemporary Anglican groups like Reform.
Does that answer whichever question you were asking?