While the orthodox remain a branch of thee Catholic Church [SINGULAR] they retained nearly th entire body of beliefs and practices of the RCC.
But much more to the point, they say that you have not done this

It’s typical Roman arrogance to assume that what you think of other churches is the only thing that matters, and what they think of you doesn’t count!
Futher and of CRITICAL importance they retained and have solid evidence of Direct Apolostolic succession. Additionlly there goal was and remains NOT a NEW independent religion; BUT rather to be a seperat branch of the CC under different leadership;
That’s not how they put it. They would say that they are and have always been the same Church that existed before the Schism, period. I’m not sure about this, because I think Roman primacy was more important before the schism than they are generally willing to admit.
BUT [crtital difference] hoding to the SAME FAITH beliefs and practices that were already acceptable to Rome, prior to the schism.
Indeed.
King Henrey has no apolostolis succession:
What is your evidence for this? As manualman pointed out, the Vatican commission that found Anglican orders to be invalid located the break some time later. I think, with all due respect, that you are misinformed here.
Unless of course you mean that King Henry himself wasn’t in apostolic succession, which is hardly the point

The bishops of the Henrician Church of England were in apostolic succession.
No affiliation with the CC
That can be disputed. He rejected the Pope’s jurisdiction. Does that actually amount to “no affiliation”? Only if you define affiliation in terms of jurisdiction. Henry would have been happy for the Church of England to be part of a family of autonomous national churches, as long as he had the final say in what went on in his lands. I do not defend this, by the way.
Proffered a seperate Bible
On what authority do you make such a serious claim? Please check this with a well-informed, scholarly Catholic. You are misinformed.
And clearly entended to NOT be a branch church of the RCC, BUT a completely different religion and set of faith beliefs and practices.
King Henry’s intentions may be clear to you, but you need to share with the rest of us the basis for this remarkable confidence of yours.
It appears to me that King Henry basically intended the C of E precisely to be a “branch church of the RCC,” with administrative control in the hands of the monarch. Since the Protestants enthusiastically supported his move toward independence, he found himself more and more allying himself with them, but he made periodic moves back in the direction of Catholicism.
Furthermore, I question whether any form of Protestantism can be said to be a “completely different religion.”
**
While the Orthodox are in Schism; the Angelians are Apostates.
Can. 751 Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith;
apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him.
**
Exactly. It is easy to show that what Henry initially did (repudiating the jurisdiction of the “Bishop of Rome”) was an act of schism. I will not deny that from your Church’s point of view (and indeed from mine) his ecclesiology was heretical as well, and certainly Protestant heresy began to influence the Church of England during his reign and was officially accepted in the reign of his son.
The charge of apostasy, however, makes no sense. Nor have you even tried to sbustantiate it. Bishop Spong can indeed be said to be an apostate. But not any Anglican of the sixteenth century–probably not the seventeenth either, but I won’t necessarily vouch for the eighteenth!
The Orthodox continue to b a branch connected to Christ through the RCC.
So you say. They say that they are connected to Christ through faith and through apostolic succession, and that they don’t need you.
Edwin