Moving Automation in Group Tracks with Folders

Wondering if there is a way I can glue some automation routed to my group channel for my synths.
So, Synths are on their own channel → routed to Synth Group
Synth Group has automation for the leads.

I’d like the automation to be glued to the synth midi events so when I move the midi events the automation is moved with it.

Is this possible? I’ve tried placing them in a folder and moving the entire folder but the automation seems independent from even the folder so I move my synths to say 9-17 but my automation in the group channel is still on 1-9.

If not, I can just copy / paste the automation but it would be great if there is a way to glue these together.