Someone said that his rabbi (maybe Sifardi) said that it is ok to eat leftover meat (dishes) from Shabbos during the 9 days.
Is this true?
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The Birkei Yosef 551/6 brings those that permit it to be eaten.
However, the Magen Avraham 551/26, Prei Megadim 551/26, Derech Hachaim 9, Mishneh Berurah 551/56 and the Aruch Hashulchan 551/24, write that it may not be eaten.
I don't know about the minhag of the Sefradim.
This is indeed true although there aren't clear parameters (until when; only for seudah revi'it/melaveh Makkah, Sun. or later). The general permissibility is not a Sefard-Ashkenaz mahloket; it is a later-day "legal loophole" discussed by many Achronim; some were Sefardic and others were Ashkenazic.
Some Sefardim accepted this "loophole" as quoted in the answer from פרי זהב and some Ashkenazim too accepted it: R. Zvi Elimelech of Dinov (Bne Yisaschar, Tammuz-Av 1:10) R. Menashe Klein (Mishneh Halachot vol. 8 §219), R. Mordechai Winkler (Levushe Mordechai vol. 3 OC §49).
For a more thorough discussion on this question see R. Ovadiah Yosef in Chazon Ovadiah Arba Taniyot (177ff.)