Corollary
Tag 04C5, permanent. Cite it as [Bourbaki, Tag 04C5].
Commutative Algebra, chapter II, § 5. Finitely generated projective modules. Invertible fractional ideals
Every invertible sub-A-module of B is flat and finitely presented. This follows from Theorem 4 (c).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.