An option with far fewer cables is the RecorderGear PR200. It records your conversation via Bluetooth. The call button in the middle of the device can answer calls on the Bluetooth-connected phone. Hold the PR200 up to your head to talk and listen, as if it's the phone. It also features a USB end to quickly access recordings on the computer. It will hold about 144 hours of conversation before it fills up the 4GB of storage. It also records like any digital recorder sans smartphone, since it has an external pin-hole microphone.
It’s a good practice for each of your team members to have their own personal business phone numbers. There are many reasons why they shouldn’t use their personal cell phone number for business, so you’ll want to give them their own phone number through your VoIP provider or phone system.

You would think there'd be app for that, but Apple doesn't allow third-party apps to access the microphone and the integrated Phone app directly. However, there are tricks within some apps and services to get around that limitation that can make you a mobile wire-tapping master.
If a phone rings once and then goes to voicemail or rings only briefly, it You can't definitively know the cause of a phone barely ringing and going to voicemail because neither a phone company nor the phone's operating system provider will tell you if your phone number is blocked.