The ornamental design for the hanging storage organizer, as shown and described.
FIG. 1 is a perspective view of the hanging storage organizer shown prior to insertion of hanger;
FIG. 2 is a second perspective view of the hanging storage organizer of my design shown with a hanger in the process of being installed;
FIG. 3 is a third perspective view of the hanging storage organizer of my design shown in use hung below a rod and holding a variety of items;
FIG. 4 is a fourth perspective view of the hanging storage organizer of my design;
FIG. 5 is a front elevation view thereof;
FIG. 6 is a rear elevation view thereof;
FIG. 7 is a right elevation view thereof;
FIG. 8 is a left elevation view thereof;
FIG. 9 is a top plane view thereof; and,
and FIG. 10 is a bottom plane view thereof.
The hangers shown in FIGS. 1-8 and variety of stored items illustrated in FIG. 3 are for illustrative purposes only and form no part of the claimed design.