Welcome to Android Central! Voicemail is controlled by your carrier, not by the phone. Check your carrier's voicemail instructions on how to save a voicemail. Also check with your carrier to see how long they will save a voicemail for.
At worst, install Call Recorder. (Test it out before you need it - there are a few different modes, and Samsung is tough to record phone calls with, but you should find one that works.) Then call your voicemail, listen to that one and, just before it starts, tap the red button (you'll get that on the Phone screen from Call Recorder). When the voicemail is finished, tap the button again. Now you have a recording of the voicemail.