Resolve Case via background workflow by "Modified by" user

Hi, 

i have custom field "Status reason" on Case and with some value of this field it resolves Case via background workflow. After succesfully ended process session is automatically created Activity on Case records ("Case resolved by Administrator") - Administrator is the owner of the workflow.

Is it possible somehow show the user who made these changes on Case record in activity? It's possibly 3 different users so change of owner of workflow it's not a solution. 

Thanks for any advice.

Alex