To save a Snap or Friend’s Story in Chat while viewing, you can press and hold on it and tap 'Save in Chat' or swipe up on the Snap and tap 'Save in Chat.'
Only photo Snaps set to no limit, and video Snaps set to loop can be saved in Chat. Look for the timer with the ∞ icon.
After saving a Snap or friend’s Story, it will appear in the chat as Chat Media. Either you or your friend can delete saved content in your 1:1 Chat.