Hello, thanks for your answer to my problem. The solution you suggest is exactly what I had tried before I opened this question in the community, but it does not seem to work for me. I am very confused. To me it seems as if there is a bug somewhere. I have the latest versions of both OS on my iMAC and IOS on my iPhone XS. So I am afraid I do not dare close a conversation in iMessage, since I want to keep the history still for some time. But it is very frustrating to see a long list of older conversations on the left side of the iMessage screen every time I want to write a message. In my inbox in MAIL on my iMAC I always move received mails to various maps to make my inbox more clean and nicer to look at. And I hoped that it should be possible to use an equivalent approach in iMessage by selecting the option 'keep history, when closing conversation' and the option 'keep forever' .