Ok.

I think I have narrowed down my problem.

First: On User B's folder, I discovered that my custom
fields were not there, so I added them to User B's folder.

Second: I realized that I had to catch the Item_Send event
to populate my custom fields. I orginally only populated
my custom fields on the Item_Write event. I guess Outlook
sends the message request, before it writes the
appointment.

But I still have one final problem... my scripts do not
run, when I open the Meeting Request in User B's inbox.

I have enabled RUN SCRIPTS IN SHARED FOLDERS in the
advanced options.. so I am not sure what else I need to do.

Do I need to create a custom message request?

Thanks for any help.