Hall departs with three goals to his name from 15 appearances, since joining Boro on loan at the end of September.
Manager Spencer Day said: “We’ve mutually agreed to terminate the loan early, so Connor can move to Brackley Town.
The Club would like to thank Connor for his time with us and we wish him all the best for the future.
Former Walsall striker Mukuna joins Farnborough for the start of the new year.
The 19-year-old was a first-year Scholar with Sutton United and is also formerly of Leyton Orient’s Academy.
Day added: “We’ve also added young Jonas Mukuna on a short-term deal so we can add cover to the squad.
Mukuna has been allocated shirt number 29.
View the updated Squad list.