Hi Girish,
Checking the MSDB is okay if the target database is also on the same server as the source. If the target DB is on a remote server it may probably need a linked server to the source server's MSDB. Hence the idea of checking the filename pattern using xp_cmdshell on a directory accessible from the target server, regardless of how the files land up in that directory - whether by FTP or by taking backup directly into that directory.
I like your idea of FTP'ing the backups to a remote target server. Please post the code for everyone's benefit.
Thanks