Learn English – Does “Let me know if you have any questions.” mean “reply only if you have a question”

Depending on the size of the vendor, your assumption may not be entirely warranted. If there are several people who may potentially receive the email at the distributor (as may happen with a shared departmental mailbox) the person who receives your email may not be aware of all the facts.

Accordingly, it may be wise to refer to the previous email at the beginning of your email (..."per the email from Mr. Customer sent yesterday regarding WidgetCo Widgets") and reiterate any key facts that you need to rely upon to make your point (..."we require, as stated previously, forty-two Widgets within a week").

By referring unambiguously to the email at the beginning, you can ensure that the person who receives your email will be reminded (if they had forgotten); will research (if they are a different person who did not initially receive the other email); or will delegate to the appropriate person (if someone else has the responsibility for this transaction).

Even if it is the same person, the phrasing mentioned above should be usable; it never hurts to ensure that your intentions are clear.

Good luck!

It depends on what the relationship is like with the recipient. If you are fairly friendly you can be less formal.

Assuming you include the e-mail you are referring to in some way, you might say:

Have you had a chance to look at this yet?

This informally conveys the sense that you know how busy they are.

For a more formal version you would probably want to write it as a full e-mail:

John/Sir/Whatever you'd normally say

I was wondering if you have had a chance to look at the e-mail below yet? [Give a reason] Our customer enquired about it earlier today.

Many thanks,

Bob