After having the cloths finished calculating in the Cloth room, I use File -> Export -> Wavefront OBJ -> Single Frame in "export Range" -> selecting the certain cloth piece only -> check the Export Options "As Morph Target" and "Include existing groups in polygon groups" and save it on a hdd.

Later then I can use the "Load Morph Target" option in the Properties tab of this certain cloth piece, load the previously saved wavefront.obj, set the new Parameter dial to 1 and the dyn cloth jumps into the previously draped pose, without the need of going through the cloth room all over again.