  In this paper, we prove a converse theorem for half-integral weight modular
forms assuming functional equations for $L$-series with additive twists. This
result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the
half-integral weight setting. Similar to their work, the main result of this
paper is obtained as a consequence of the half-integral weight Petersson trace
formula.
