After　the　establishment　of　the　finite　embeddability　property　for　integral　and　commutative　residuated　ordered　monoids　by　Blok　and　Van　Alten　in　2002,　the　finite　embeddability　property　for　some　other　types　of　residuated　ordered　algebraic　structures　have　been　extensively　studied.　The　main　purpose　of　this　paper　is　to　construct　a　finite　quantale　(X)　over　cap　(F)　from　a　finite　partial　subalgebra　F　of　an　increasing　quantum　B-algebra　X　so　that　F　can　be　embedded　into　(X)　over　cap　(F),　that　is,　the　class　of　increasing　quantum　B-algebras　has　the　finite　embeddability　property.