What is the significance of the inscription in the Biblia Hebraica Stuttgartensia between the Psalter and the book of Job and what is the proper translation?
The text in question is an end-note by an editor, fairly typical of printed editions of Biblia Hebraica Stuttgartensia. Thanks to a friend whose Hebrew is fluent (mine is not), I learned that the meaning is quite straightforward. It refers to the Book of Psalms. It simply summarizes the number of verses and sections:
sum of the verses of [the] book
two thousands and five hundred
and twenty and seven
and sections 19
The "sections" apparently refers to a reading schedule. Thanks to @Magicker72 at Mi Yodeya, I was able to discover what this means. It is an old division of the Hebrew Bible, no longer in use, into sections for scheduled reading.
Tanach Yomi helpfully provides a list which includes the 19 sedarim [divisions] for Psalms, with starting points at: 1:1, 11:7, 20:10, 29:11, 35:28, 41:14, 49:19, 57:12, 67:8, 72:20, 78:38, 84:13, 90:17, 101:1, 105:45, 111:10, 119:72, 128:6, and 140:14.