Since it's on one ticket/reservation the BA EDI agent will see something similar to:

BA1234 -LHR C 0900 1000
JJ3455 LHR-GRU J 1100-1500

...on the check in screen. They'll probably just tell the system to print the bag tags and send them on their way. The system's default is to generate tags for the itinerary on the screen. The agent would have to proactively "short check" the bag to LHR which there's no reason for them to do so.

So, you should be fine.

Interline: Airline "A" connecting to Airline "B"
Codeshare: Airline "A" connecting to Airline "B" but flight "B" carries a flight number for Airline "A". (It's really an interline journey though)