Masks can be selected and copied to position properties or other layers. For the size and placement of the mask or shape layer path to match up when it is added to a new layer, the original layer cannot be scaled, rotated, or moved from its original default position because vector paths are based on layer space, not comp space.
I find the most reliable way to copy a path is to set a keyframe, then cut it. Then select the new layer, select the pen tool, click once anywhere in the comp to start a new path, then paste. Ctrl/Cmnd + x then add a point and Ctrl/Cmnd + v always works.
You can also select a motion path and copy and paste it using the same trick. You just need to make sure you have all of the keyframes in the motion path selected. This will create an open mask path or an open path in a shape layer.
You can paste a Mask Path onto a Text Layer BUT not with a Shape Layer Path.
To work around this, create a temporary/dummy Mask Path on your Text Layer. You then paste the Shape Layer's Path onto the Text Layer's Mask Path. To create a LIVE link between the Mask Path and the Shape Layer Path, you can create an Expression to link the Mask Path to the Shape Layer's Path. HTH
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