Firstly, it's important to understand that moving and approving nodes are two entirely separate operations. They cannot be done together.
"Note that you must never attempt to move and approve a node in the same step! Or even two steps!"
Armed with this information you can probably now answer the question for yourself:
Whenever I move a post, I normally /msg the OP to this effect: I do this as a courtesy; it is not a requirement. I never advise OPs of node approval.
Finally, please consider the wording, and hence the tone, of your questions. Something like "Would it be too hard for moderators ...?" rather suggests that you think that moderators are lazy. Of course, that may not have been your intent at all; however, to demonstate the point, consider this:
"Would it be too hard for you to post a link to the node you're commenting on?"
Compared to this:
"Please provide a link to the node you're commenting on."
Both convey much the same information, i.e. you've failed to tell us what post you're referring to; however, the former has a nasty undertone whilst the latter is a polite request.