There is no single string that will work for all server instances, unless it always directs to one specific server - in which case you need two things:
1) The IP address or host name of the server: mySQLServber.mydomain.com for example.
2) The server instance will need to be configured to accept remote connections - and not all are for security reasons.
In addition, you will almost certainly need actual login information: it's very unusual for remote connections to accept integrated security.
If you are trying to work to his local instance, you need to find it as part of your installation program - you cannot assume that it shares any name or IP with yours. You should also test the connection and install the DB at that point as well.
Your existing connection data assumes that there is a DB server on the current machine - if that isn't the case it will fail, but we can't tell you what to use instead! We can't even tell if he has SQL Server installed!
If you are only using the DB as a single user each time (rather than sharing data) it's probably a better idea to use a single user DB such as Access or SqLite instead of SQL Server - that way you only need to add the DB itself to your installation and the DB engine will be included in your app assemblies.
You may find this helps if you are sharing a number of DB related apps with your friend:
Instance Storage - A Simple Way to Share Configuration Data among Applications[
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