For On-premise customers.
your connection string can be found in
For AC10 systems
%localappdata%\OCiSystem\AC10\app.config
For SAM systems
%localappdata%\OCiSystem\SAM\app.config
For Hosting customers
For AC10 systems
%localappdata%\OCiSystem\AC10R2\app.config
For SAM systems
%localappdata%\OCiSystem\SAMR2\app.config
you can copy this file and place it in the similar location on the different PC.
Note that %localappdata% is a windows shortcut to a folder in the profile. it will be different on each PC.
in windows explorer type the words in the address bar