If you recently restored or updated your iPhone, your network setting may have been affected and may be causing “iPhone voicemail error try again later.” Please reset your network settings. Go to Settings > General > Reset > Reset Network Settings Enter your password. Press Reset network setting in red font. The phone will automatically reset it. After it restarts, your phone then tries voicemail again.
To send to an email address with the message attached, check the box next to Attach new voicemail messages and send via email.

Traditional voicemail services once offered this feature, but visual voicemail (with a visual interface that lets you access messages directly) has mostly eliminated that possibility. If your phone does not have visual voicemail, and you have to call an inbox to hear your messages, you may still be able to use this feature.
An alltime classic technique was offered by Thomas J. Elijah, III, of Elijah & Co. Real Estate, at a SalesMasters meeting. He said to leave a partial message that includes your name and phone number, then pretend to get cut off in midsentence, as you’re getting to the important part of the message. “Cut it off in midword,” Elijah says, “it works like a charm because the prospect can’t stand not knowing the rest of the information, or thinks his voice mail is broken.”