The ornamental design for part of a lightstand with charger, as shown and described.
FIG. 1 is a front elevational view of a light stand with charger showing my new design;
FIG. 2 is a rear elevational view thereof;
FIG. 3 is a left side elevational view thereof;
FIG. 4 is a right side elevational view thereof;
FIG. 5 is a top plan view thereof;
FIG. 6 is a bottom plan view thereof
FIG. 7 is a horizontal cross-sectional view thereof, taken in the direction of line A-A of FIG. 1;
FIG. 8 is a front and right side perspective view thereof; and,
FIG. 9 is an additional front and right side perspective view thereof, with the broken line disclosure of an electronic device being for illustrative purposes only and forming no part of the claimed design.