This could be a tough request due to groups being specific to projects. Trying to differentiate between existing groups in the destination project & new groups being imported would be difficult when the naming is the same. i.e. "Group 1" in destination and importing "Group 1" from the source timeline.
Even grabbing stills treats the Groups as seperate stills from Clips & Timeline stills.
You can collapse the groups if you need to transfer timelines but I know this is not what you are asking for.