Customer calls (Incoming call) on the IVR application -> make outbound call to agent is logged in on PSTN (mobile phone)-> Once agent picks the call patch the customer call with the agent. Call control staying on the AAEP

How can I do the above?
Outbound call can be made using LaunchVXMLCall/LaunchCCXMLCall but how can the customer called in be patched with agent on mobile number making it one on AAEP?

This is a duplicate of the other post.

A briged transfer is the simplest method to accomplish this.

https://www.w3.org/TR/voicexml20/#dml2.3.7 see 2.3.7.2 Bridge Transfer