Hi - you can do this with the Apply Symbology from Layer gp tool. it will pull the label classes from a layer already in the map or from a saved layer file.
Perhaps the fact that it handles that could be made more explicit and intuitive in the tool name, in the parameters, or in the way it's accessed (from labeling, too, rather than just symbology), and include an option to transfer only label classes? Just a thought. I thought that tool did labels, too, but even when I opened it and looked, it didn't seem like it would to me. It's not mentioned in the in-app help; other than that one bullet on that page you linked, there's no indication that labeling is transferred.
@JonathanNeal@WendyHarrison also, it's not always desirable to copy over the symbology (or whatever else that tool copies and doesn't tell you about). Sometimes you just want the label classes, or a few of the label classes. It also seems silly to have to head to the symbology pane or the GP tool for copying label classes.
Seems the following ideas request similar functionality and could probably be all merged together:
@wayfaringrob Yeah mostly similar to this issue. We do not have any Geoprocessing tools that run between maps, but the other two ideas above will be accomplished in the near term. We are working on a new tool that will let users take layer properties they want (Near term)
Currently Apply Symbology from Layer tool will move Labels and other properties (Mostly wanted). But, the more desired approach is to allow users to chose the specific properties they want and how they are applied to the layer.
I hope this helps, it is on our radar, desigin is in, and scheduled on our 3.2 release.
