Forget about messing around with apps. There’s a powerful voicemail handling system built into nearly every big carrier today — and that system almost always includes a system for recording a voice message and sending it directly without ringing the target phone. I will walk you through the process of doing this on Straight Talk (since that happens to be my carrier) but most carriers will have similar systems.
RecordiaPro has options for recording both in the US alone (starting at $29.99 for 120 minutes) or worldwide ($40 for 190 minutes). Create an account before you call, put RecordiaPro's number in your contacts, and use it when you call out or silently add RecordiaPro to existing calls. For $36 per year, it will provide a number you can hand out to take future calls that get auto-recorded. Future recordings are available in your account.

Voicemail is a method of storing voice messages electronically for later retrieval by intended recipients. Callers leave short messages that are stored on digital media (or, in some older systems, on analog recording tape). Originally, voicemail was developed for telephony as a means to prevent missed calls, and also to facilitate call screening.
Voicemail is not working on your iPhone and you don’t know what to do. It’s incredibly frustrating when voicemail won’t work, especially if you were expecting an important phone call from a friend or family member. In this article, I’ll show you what to do when your iPhone won’t play voicemails so you can fix the problem for good.