The ornamental design for a "telephone handset hang-up device or similar article", as shown and described.
FIG. 1 is a bottom, front, and right side perspective view of a "telephone
handset hang-up device or similar article" showing our new design in full
lines, with the broken line matter being for illustrative purposes only
and forming no part of the claimed design;
FIG. 2 is a left side elevational view thereof;
FIG. 3 is a rear elevational view thereof; and
FIG. 4 is a bottom plan view thereof.
The broken line showing of environmental association in FIG. 1 is for
illustrative purposes only and forms no part of the claimed design.