To determine the number base in which \(263 + 441 = 714\), let's check the calculation in different bases.

Base 12 Calculation:
- Convert \(263_{12}\) to base 10:
\[
263_{12} = 2 \times 12^2 + 6 \times 12^1 + 3 \times 12^0 = 2 \times 144 + 6 \times 12 + 3 = 288 + 72 + 3 = 363_{10}
\]
- Convert \(441_{12}\) to base 10:
\[
441_{12} = 4 \times 12^2 + 4 \times 12^1 + 1 \times 12^0 = 4 \times 144 + 4 \times 12 + 1 = 576 + 48 + 1 = 625_{10}
\]
- Add the results in base 10:
\[
363_{10} + 625_{10} = 988_{10}
\]
- Now, convert \(988_{10}\) back to base 12:
\[
988_{10} = 7 \times 12^2 + 1 \times 12^1 + 4 \times 12^0 = 714_{12}
\]

Since the equation \(263 + 441 = 714\) holds true in base 12, the correct answer is A. 12.