<p>We have proved the global correctness theorem to the second mixed problem for a linear general telegraph equation with variable coefficients in a half-band of the plane. By global correctness theorems to mixed problems for partial differential equations, we mean theorems with necessary and sufficient conditions for Hadamard correctness: existence, uniqueness, and stability of classical solutions. Riemann’s formulas for a unique and stable solution and a correctness criterion to this mixed problem in the set of twice continuously differentiable functions are derived. Its correctness criterion is established from matching conditions and smoothness requirements for the initial data, boundary data, and the right-hand side of the equation. The necessity and sufficiency of integral smoothness requirements on continues right-hand side of the equation is proved by the correction method of test solutions into classical solutions. These results are obtained by new “method of auxiliary mixed problems for wave equations on the half-line” and new “implicit characteristics method” without explicit extensions of the problem data.</p>