不定式 to put back the magazine 作动词remember的宾语；
when you have finished reading it 是时间状语从句,修饰动词put back.
记住看完后把杂志放回原处.remember做主语还是谓语动词？缺少了一个成分啊作谓语动词，此句是祈使句，主语省略了