Yes! From the live video or replay full screen mode, click or tap the share icon {{ twtr-rte-icon:outgoing }} then choose between the following options:
Click or tap Share Live (when live) or Share From Beginning (when in replay mode) to Tweet, Direct Message, or copy the link of a full live video or replay from the beginning.
Click or tap Share from… to Tweet, Direct Message, or copy the link of a live video or replay starting at a point chosen using the selection bar.