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This project: The Ultimate Google Voice How-to Guide (2014 Edition)
Filters are your friends
The best way I've found to get messages is by using email filters. This way, any message that Google Voice gets comes into my associated Gmail account, a filter (or rule, for you Outlook folks) runs on it, and the message then gets forwarded to one or more additional accounts or services.
First, switch on over to the Gmail account associated with Google Voice. If you've gotten any voicemail or SMS messages since you enabled notifications, you'll see them in your Gmail inbox.
Find the Options gear at the far right of the screen, and select Mail Settings from the drop-down menu. Next, click Filters to put yourself on the Filters tab.
Here, you'll add two new filters. The first is going to have a From field value of "email@example.com" (without the quotes). Click Next Step, and then check "Forward it to:".
It's here where you'll fill out your alternative email forwarding address. If you don't have any authorized addresses, adding them is easy. Just click "Manage your forwarding addresses," enter your desired address, and Gmail will send a confirmation email to that address. Once that confirmation has been clicked on, Gmail will know you're the rightful owner of the email address you've registered, and will let you set forwarding.
The "firstname.lastname@example.org" will handle voicemails. Add a second filter that matches a From field value of "@txt.voice.google.com" and forward this to your alternate email address as well.
When you're done, you should have two filters that look something like this:
So there you go. Your voicemails and texts can now be sent to any email address you want.
Next in our series, we begin our Google Voice for Small Business how-to guide with Google Voice: how to consolidate your virtual phone numbers