Start job from another SQL server instance
You probably don't want to grant direct access to sp_start_job or sp_stop_job, or even grant access to a range of SQL Agent functionality via SQLAgentOperatorRole, to either NT AUTHORITY\NETWORK SERVICE or MyDomain\ServerA$. Doing any of those combinations would, at the very least, allow any process running as NT AUTHORITY\NETWORK SERVICE on ServerA the ability to start and/or stop any job on ServerB.

Using Module Signing, you can set up very granular permissions such that MyDomain\ServerA$ (or any login or role, or any combination of those) can only start and stop that one particular job.

USE [msdb];
GO
CREATE PROCEDURE dbo.StartStopJobX
(
  @Operation VARCHAR(10) = 'start'
)

AS
  IF (@Operation = 'start')
  BEGIN
    EXEC dbo.sp_start_job N'{job_name}';
  END
  ELSE
  BEGIN
    EXEC dbo.sp_stop_job N'{job_name}';
  END;
GO


CREATE CERTIFICATE [SqlAgentPermissions]
 ENCRYPTION BY PASSWORD = 'change_me'
 WITH SUBJECT = 'Allow low-priviledged accounts to start/stop certain jobs',
 EXPIRY_DATE = '2099-12-31';

ADD SIGNATURE
  TO dbo.StartStopJobX
  BY CERTIFICATE [SqlAgentPermissions]
  WITH PASSWORD = 'change_me';

CREATE USER [SqlAgentPermissions] FROM CERTIFICATE [SqlAgentPermissions];

ALTER ROLE [SQLAgentOperatorRole] ADD MEMBER [SqlAgentPermissions];


Now all you need to do is:

GRANT EXECUTE ON dbo.[StartStopJobX] TO [MyDomain\ServerA$];