Pope Urban II [Council of Piacenza, cap. x; cf. Can. Ordinationes, ix, qu. 1] says: “We command that persons consecrated by bishops who were themselves consecrated according to the Catholic rite, but have separated themselves by schism from the Roman Church, should be received mercifully and that their Orders should be acknowledged, when they return to the unity of the Church, provided they be of commendable life and knowledge.”
From the Summa:
Spiritual power is twofold, the one sacramental, the other a power of jurisdiction. The sacramental power is one that is conferred by some kind of consecration. Now all the consecrations of the Church are immovable so long as the consecrated thing remains: as appears even in inanimate things, since an altar, once consecrated, is not consecrated again unless it has been broken up. Consequently such a power as this remains, as to its essence, in the man who has received it by consecration, as long as he lives, even if he fall into schism or heresy: and this is proved from the fact that if he come back to the Church, he is not consecrated anew. Since, however, the lower power ought not to exercise its act, except in so far as it is moved by the higher power, as may be seen also in the physical order, it follows that such persons lose the use of their power, so that it is not lawful for them to use it. Yet if they use it, this power has its effect in sacramental acts, because therein man acts only as God’s instrument, so that sacramental effects are not precluded on account of any fault whatever in the person who confers the sacrament.
On the other hand, the power of jurisdiction is that which is conferred by a mere human appointment. Such a power as this does not adhere to the recipient immovably: so that it does not remain in heretics and schismatics; and consequently they neither absolve nor excommunicate, nor grant indulgence, nor do anything of the kind, and if they do, it is invalid.
Accordingly when it is said that such like persons have no spiritual power, it is to be understood as referring either to the second power, or if it be referred to the first power, not as referring to the essence of the power, but to its lawful use.
Likewise, since Leo XIII thought it necessary to rule on Anglican orders, beforehand there must have been valid reason to accept their orders. The Orthodox, on the other hand have preserved the various rites (unlike the Anglicans) and have not been re-ordained upon conversion.