Yes, you have to copy the shape’s path attribute and paste into the other shape group’s (or layer’s) position property.
So, you would have to disclose the dotted line’s shape path property group. Target the path property (not the property group, but the enclosed property inside) and copy it. Then you can choose if you to paste it to a shape object (parametric shapes only!), shape group or shape layer.
Each shape group has a transform properties group. Select position inside that transform group and paste your path there. If you select position for the whole layer (instead of a shape group) the whole layer will follow that path. You will probably need to adjust the group’s (or layer’s) anchor point afterwards.
Is it clear?
Shape layers are terrific, but of course they are a whole new world and it takes some time to get used to all the possibilities.