Do we need an article here:
Send him an / - e-mail. ?
I thought there should be an indefinite article, but was surprised to see no article in the definition (see the link below):
[+ obj] : to send __e-mail to (someone)
Is e-mail countable or uncountable?
If I were a native speaker of English, I would never shut up. :-)
When the word appeared, some argued that it should be uncountable like mail and we should say two items of email, but this was ignored and individual messages are countable. However, your example is the same as their definition 2b, which has an article.