You can forward a message from a chat conversation to your Gmail Inbox, so that the message will still be available if it is removed from Chat. When you forward a message, the selected message and the last 4 messages in the thread will be forwarded, including any images and links to shared documents.
To forward a message to your Inbox:
Locate the message you wish to forward
Position the mouse over the message, then click on the ellipses on the toolbar that appears
Choose Forward to Inbox
The message will be sent to your Inbox and will be named Fwd: Chat with (name) 'content' where name is the person you were chatting with, and content is the text in the message you forwarded to your Inbox.
Note that the Open Message link will return a Message not found error if the message has been removed in Google Chat.Â