In AM, on the right, click open. Get the project that has the stuff. Unfortunately you can't use templates, BPNs, PLPs, or PLCs.
Now you have the local atts on the left and the "guest" atts on the right. Select the atts you need and either 'Append' or 'Overwrite' them into the local project using the buttons in the middle.
The difference between Append & Overwrite is important. Append will put the new atts at the end of the list with a new ID. This will likely be different from the ID in the guest project. Overwrite will maintain the ID of the new att, and will write over a local att of the same ID if there is one. If there isn't one, the new just gets dropped into place in the list.
It sounds like you should Overwrite in this case. Probably the local project and the guest originated with the same template, and their atts should have the same IDs. So if you deleted the Composite that had ID 9, you should be able to overwrite with the guest ID 9 to get back where you were.
IDs become important because they are the way that AC actually thinks about attributes. For example, bringing in fills with the same name but different IDs can cause problems for composites and materials, because those atts pick up their fills based on the ID. Objects' default attributes can get messed up this way too. Live and learn.
Changing IDs deliberately is another topic. If Link is around, he has investigated this thoroughly and can tell you more.
HTH,
