asterisk sip calling, how to handle when receiver is voicemail box?

how to better handle when sip termination to an answering machine / voicemail box? in our service, user A records voice message for user B our asterisk box uses sip to deliver the voice message to user B (usually a mobile phone) caller id set to user A (user B can see incoming call from someone s/he recognizes) too many times, instead of user B hearing the voice message, the call gets routed to user B voicemail box and user B never hears user A sent a voice message. with our sip providers, either they auto disconnect as soon as user B voicebox beeps prompts to leave message, or the outgoing user A voice message is completed before the user B voicemail box beeps to record. got to think of better way to handle this, too many user A voice message not being delivered to user B or to their voicemail boxes :(