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No, this has no relation with the movie or the previous tv series at all.

This series follows more closely to the original manga than it's predecessor, though there are still some cuts from the original source material throughout the series. Several characters from the original manga that were left out of the previous series are used for this series, just as how there are numerous characters from the previous series that are exclusive to that series and are not used here (along with a few minor manga characters that were used in the first series but not here). Also while episodes 2-14 use similar material to the previous series, there are notably a few plot changes as it reflects based on what occurred in the manga and not the previous series. Episode 15 would officially start with the material from the manga that was never used before. Also FMA2003 has a more dramatic tone to it and FMAB has more of a action adventure feel to it.