Linked server works locally from SSMS but not from remotly connected SSMS

When trying a simple query like this remotely from SSMS:

SELECT * FROM [LinkedServer1].[Database1].[dbo].[Table1]

it fails with :

Msg 18456, Level 14, State 1, Line 1
Login failed for user 'NT AUTHORITY\ANONYMOUS LOGON'.

but when I log on to the SQL Server that has the linked server setup on it, open up SSMS and run the same query it works.  I think this is because it is using my windows credentials properly and not trying to use Anon.

How can I make my remote SSMS connection work?

Thank You