Clicking "Yes" works in a single user environment.
In a multi-user environment, FMP doesn't need to know "Yes" as much as "Who".
When the "Pick" button is selected, I would use that click to set a field (not on the layout) to
SetField( Sessions::Picklist ; Sessions::Picklist & "CR" & Get(accountname))
CR being Carriage Return
When they want to see what they have picked...do a find in the Picklist Field for their account name.
Your Yes/No box can now just be a calculated field based on whether or not their account name exists in the Picklist field.
Note that none of this is global...though depending on how slick you want the interface to be, you could set a primary key to their account name and use that to filter a portal from a self-joined table...
Thanks Eric. Your suggestion was super-helpful, and I changed the checkbox from a simple "Yes" to being associated with each user's accountname.