“Would you mind forwarding me his reply?”

A coworker sent an important e-mail to a client. You ask her if she got a response from them, and she says that she did. You want to read what they said, so you ask your coworker:

Would you mind forwarding me his reply?

Would you mind (doing something)?

"Would you mind ___ing?" is a good way to politely ask for something that isn't too much trouble for the other person. Some more examples:

Would you mind giving me a hand with this?

Excuse me. Would you mind watching over my stuff for me for just a minute?

Would you mind sending me a list of everyone who's coming?

forward (someone) (an email message)

When you "forward" someone an e-mail message, it means that you send them a message that someone else sent you before. Most e-mail software includes a button for this that's marked "Forward" or "Fwd".

Notice that there are two correct ways to use "forward". One is "forward (someone)(a message)":

I forwarded Jane the invitation that you sent me.

The other way is "forward (a message) to (someone)":

I forwarded the invitation you sent me to Jane.

The choice of which one to use depends on what you're talking about. If the topic of the conversation is Jane, I would use the first example. If the topic is the invitation, I'd use the second.

(someone's) reply

A "reply" is an answer to a message. When you send a message to someone and they send one back, that return message is their "reply".

This word is similar to "response", and in many situations you can use both. But a "response" is more general than a "reply". A "response" to a message can be a written reply, something that the person said, or even an action like smiling or crying. But a "reply" is usually just a written response.