When you say you have imported multiple parts into different "models", do you mean "models" in the ABAQUS/CAE terminology?
If you have multiple models in the one cae database you can easily copy objects from one model to another (use the menu Model-Copy Objects). You can copy parts, materials, sections, etc etc.
If you have your parts in separate /CAE databases, you can export the parts as SAT files (File-Export-Part) and then import them into the required /CAE database.