Use Live-to-VoD

The Live-to-VoD feature enables you to convert live streams to video-on-demand assets.

HLS

For Live-to-VOD to properly function, the encoder must insert an #EXT-X-PROGRAM-DATE-TIME tag after a discontinuity event. For example:
#EXT-X-PROGRAM-DATE-TIME:2017-01-19T08:04:00.624Z

The EXTINF tag is also mandatory for Live-to-VOD.

DASH

For DASH, Live-to-VoD is supported only for sequential segment indexing and not for time-base indexing.