Windows Authentication for a non-local non-domain Login
Create matching usernames and passwords. It really is that simple. For your example, create an account for User1 on Server1 with the same password as on PC1.

Just in case this is an issue you're having with connecting SSMS with a non-domain account, that requires jumping through an additional hoop. Some applications don't support stored usernames and passwords via the windows credential store. SSMS is one of them.

I have a bunch of runas shortcuts to deal with connecting SSMS to a variety of servers in different domains:

C:\Windows\System32\runas.exe 
/netonly 
/user:DOMAIN\USER 
"C:\Program Files (x86)\Microsoft SQL Server\100\Tools\Binn\VSShell\Common7\IDE\Ssms.exe"


You could also make use of the SysInternals ShellRunAs extension.