Completion of SQL Job triggers start of job on a different SQL Server
If you're on SQL Server Enterprise Edition:

You could set up a Data-driven subscription in SSRS. On your database with the FTP/Import Job, the system database MSDB contains a table called sysjobhistory. On your SSRS server, set up a Data-driven subscription to run when the step in your FTP/Import job reports success to this table.

Instructions for setting up a Data-driven subscription in SSRS: Books Online

If you are on Standard Edition:

Please use a linked server as outlined by Martin Smith here:


  Data Driven subscription is an Enterprise Edition feature. Just creating a regular subscription with a schedule in the past and calling EXEC LinkedServer.ReportServer.dbo.AddEvent @EventType='TimedSubscription', @EventData='whatever' would do what they need. 


To implement Martin's suggestion, use the SQL Server agent job that is created automatically by SSRS when a subscription is created. The job's name will be capital letters and numbers, separated by hypens. 

You should create this subscription, but then alter the job itself to have a schedule in the past, where it will not run. When you call this dbo.AddEvent over your linked server, you can add a new run time to this job