What department did he put through to?

Almost. Хотя, трудно сказать навернянка потому, что один элемент здесь упускается - то есть, "<em>who</em> did he put through (to whatever department)?"

Например,

<em>What department did he put you through to?</em>

<em>What department did he put her through to?</em>

может быть, даже, <em>What department was he put through to?</em>