Finding messages, files, and users using search tools in Microsoft Teams Free
Just to avoid any confusion. Searching doesn't work in chats created in Skype and then migrated to Teams. The search function only works in native Teams chats. This issue was acknowledged by Microsoft as a known limitation in Skype created chats.
Here is the quoted answer received from Microsoft
"You are correct, the in-chat search does not work correctly in some migrated Skype chats. This is a known issue and we are working on fixing these chats. It's just there's a lot of Skype chats and the process continues to take some time. And unfortunately there is no immediate workaround available for the affected chats except to wait. Creating a new chat could be an option too, but I do understand this is not the best way if there's extensive chat history in the old chat."