We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal -categories is represented by a strong symmetric monoidal left Quillen functor between simplicial, combinatorial and left proper symmetric monoidal model categories.
"Presentably symmetric monoidal $\infty$–categories are represented by symmetric monoidal model categories." Algebr. Geom. Topol. 17 (5) 3189 - 3212, 2017. https://doi.org/10.2140/agt.2017.17.3189