We prove the Yamada-Watanabe theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called "method of the moving frame" allows us to reduce the proof to the Yamada-Watanabe theorem for stochastic differential equations in infinite dimensions.
"The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations." Electron. Commun. Probab. 18 1 - 13, 2013. https://doi.org/10.1214/ECP.v18-2392