Re: Is this sentence correct?
I think that we've had a couple of discussions about the use of "should" with "that" recently. I can tell you that in BrE, it sounds much better without it. However, there's a more basic problem with your sentence. Why would the intern "type the report on his desk" (where "his" refers to Mr Hampton)? Surely he/she will type it at his/her own desk and then deliver it to him.
Originally Posted by juliana0403
Mr Hampton asked that his intern type the report and have/put it on his desk by the end of the day.
Mr Hampton asked his intern to type the report and have/put it on his desk by the end of the day.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.