Query Linked Access database on network share via SQL Job Agent
Note: SQL Server Agent itself does not access the share

It depends on how you have mapped linked server security between local and remote credentials. SQL Server Agent running as local system will connect to SQL Server, which then accesses the share based on linked server credentials. 

SUSER_SNAME will be different of course in this case to when you run it.

Options:


add a linked server login mapping for "local system"
configure all local credentials to use one remote login
look at SQL Server Agent proxy accounts for the job step (changes SUSER_SNAME)