Using Existing Time Machine Backup over Time Capsule

Question

I have an external 2TB drive that I've been using for Time Machine Backups directly connected to my Mac. I've recently gotten a Time Capsule and would to continue backing up with the existing backup, so that I keep the history I already have and do not need to start from scratch.

I'm able to see the drive and can see the Backups.backupdb directory, as well as the subdirectory that contains my backup, but if I try to backup, it starts from scratch on the drive in a toplevel directory (/Volumes/T2/mbp instead of /Volumes/T2/Backups.backupdb/mbp). This also does not look like the same type of content of the backups made from the direct connect drive.

Is there some way to use the existing backup and continue from where I was?

Is this a safe and reliable method for using Time Machine?