The ornamental design for a liquid soapdispenser part, as shown and described.
1.1 is a perspective view of a liquid soap dispenser part, showing our new design;
1.2 is a top view thereof;
1.3 is a front view thereof; and
1.4 is a side view thereof.
The broken lines shown in the drawings of the liquid dispenser part are for the purpose of illustrating environment and form no part of the claimed design.