The ornamental design for a stabilizedconnector with integratedblock valve, as shown and described.
FIG. 1 is a front view of a stabilizer connector according to my invention;
FIG. 2 is a rear view thereof;
FIG. 3 is a bottom view thereof;
FIG. 4 is a top view thereof;
FIG. 5 is a left side view thereof;
FIG. 6 is a right side view thereof; and,
FIG. 7 is a perspective view thereof.
The broken line showings in the figures is included for the purpose of illustrating portions of the stabilized connector and forms no part of the claimed design.