This Magnificat is attributed to Buxtehude mostly on the basis that it appears in Gustav Düben's collection of scores. The score has Buxtehude's name on it in square brackets but if you look at the name it's very obviously been added by a later hand. Other than that the sole basis for the attribution seems to be that Bruno Grusnick who edited the first modern edition of Buxtehude's works said it was by Buxtehude. It's hard to see why he believed this as it doesn't resemble anything that Buxtehude ever wrote but Grusnick's assertion was the received wisdom until Martin Geck pointed out the obvious.
Whoever wrote it it's a charming piece (SSATB, with SSATB soli and instruments) that's greatly loved in Germany but for some odd reason or another is largely unknown outside of there. It's written in the Franco-Italian middle baroque bel canto style popularised by Carissimi and Lully and has some delighful triple time melodies. As you might expect from bel canto music there's a fair amount of diatonic harmonies and a very clear structure laid out in sections. The scoring is for two violins, two violas, cello, bass, and continuo. Enjoy :-).