If you are asking if you can transfer/copy those shows over to the new Tivo? Then, Yes. as long as all the boxes involved are Tivo subscribed (lifetime/month/year.) Also as long as the shows are unprotected. Just make ALL the Tivos in your account have connected to Tivo service AFTER the new box was added/updated.
Original S1 (Recycle Heaven)
Series 2 (PLS, sold)
TiVo HD (XL, PLS, "652")
Juliet Basic (4XL, PLS)
The TiVo Apocalypse begins on Sat 2013 Feb 16 00:00 GMT!