I wonder, though…
Orthodox Churches do have an annulment process, although it is rarely used.
The Orthodox have ecclesiastical divorces, which are not at all annulments.
For an Orthodox marriage to actually be
invalid (i.e. what we would term a decree of nullity) it woud have to be that the priest did not perform the marriage properly. It is the priest that confers the sacrament. Very rare indeed that this would be invalid.
An Orthodox who married outside the Orthodox Church is excommunicated and that marriage would not be considered valid, but using terms like “valid” isn’t really the way the Orthodox would view it.
If an Orthodox tribunal had declared a previous marriage to be invalid, would it also be considered so by the Catholic Church, as the Church accepts the ecclesiastical authority of the Orthodox, with regard to their own members.
I don’t believe this would be the case at all.
The Orthodox have many reasons for an ecclesial divorce that the Catholic Church would not accept as nullity grounds. It may or may not accept a determination of invalidity based on the priest who administered the sacrament.
Whatever finding an Orthodox priest or what they have equivalent to a tribunal would be looked at but the finding would have to be from the Catholic tribunal. If they concurred, it is the Catholic tribunal decision that actually makes the Orthodox free to marry a Catholic.
The Catholic Church would definitely affirm what we call “lack of form” but it would have to go through the Catholic marriage tribunal, not an Orthodox process.
An example would be an divorced Orthodox man, who had been granted an annulment by the Orthodox Church, desiring to marry a Catholic. According to the pastoral agreements in place in the US regarding Catholic-Orthodox marriages, this wedding would usually take place in the Orthodox Church. Would the woman be free to marry this man, in the the Orthodox Church (or Catholic, for that matter)?
Only after a Catholic marriage tribunal found the Greek Orthodox man free to marry.
I have never heard of an Orthodox marriage being found “invalid” by the Orthodox, because again remember the
priest confers the sacrament same as baptism, chrismation, eucharist, etc. It would be rare, rare, rare, that the priest did so invalidly.