That'd be a nice feature, but unfortunately, you cannot.
It can be some small help to pop up the object info palette and then you can click the part label. That, at least will give you the exact height of the part so that you can duplicate it on your new layout.
Thanks, Phil. At least I know I wasn't overlooking something simple. I had been doing what you suggested. It's just that, as you know of course, it gets tedious having to set size, then set bg fill, then copy-and-paste an object group for each layout after they all have been created. Particularly if there are quite a few of them. And it is easy to miss something. Then if you decide to change something later...
Thank you for your post.
The answers provided by PhilModJunk are correct (Thank you!).
Although I'm 99% sure what you want to do, I thought it would be best to mention to other users reading this post that FileMaker Pro does have the ability to duplicate a layout. This way, you have the fields, size, background fill, etc. This way, instead of copying the background color, copying the size of the layout, etc., you can delete the fields in the duplicated layout, and copy the fields from the other layout into this new layout. It may save time.