If the boosters want to send that money to the newly created booster program for the other campus, they can, but they're under no obligation to do so. If the existing boosters want to be neighborly and helpful, they CAN send money to the new program if they want, and many will choose to do so, but again, there's no obligation.
(Of course, making sure BOTH booster programs are fully incorporated as 501c3 non-profits helps)
Think of it this way: if a kid moves into your program from the next town over, does their booster money follow them? Do they cut a check and let the kid bring it with them? Of course not - and it's the same for multiple high school districts.