While connectors in Microsoft Teams can deliver content and service updates directly from third-party services into a Teams channel, they primarily post these updates directly into the chat stream. They do not have the capability to update messages or send messages as replies to existing ones.
To develop a notification integration with Microsoft Teams where messages can be updated and some messages can be sent as replies to existing ones, you would need to create a bot.
Document Ref: https://learn.microsoft.com/en-us/microsoftteams/platform/bots/how-to/update-and-delete-bot-messages?tabs=dotnet
Sample Ref: https://github.com/OfficeDev/Microsoft-Teams-Samples/tree/main/samples/bot-conversation
Thanks,
Prasad Das
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