You can use this method on iPhones and iPads running iOS 14 or later.
If you have more than one conversation pinned, then tap Edit >Edit Pins in the top left corner of your screen. Once you do that, tap the minus icons to unpin conversations.
You need to be using macOS 11 or later to have this feature.
You can also drag the pinned message down to your list of other messages. [2] X Research source
If you have a Samsung phone, this method will work for you if you’re using the default Samsung Messages app.
This method will work for all Androids other than Samsung using the default texting app.
You can use this method on iPhones and iPads running iOS 14 or later.
To pin multiple conversations, tap Edit > Edit Pins and tap the pin icon next to each conversation you want to pin to the top. Alternatively, swipe right across a conversation to pin it.
You need to be using macOS 11 or later to have this feature.
If you have a Samsung phone, this method will work for you if you’re using the default Samsung Messages app.
This method will work for all Androids other than Samsung using the default texting app. You can only pin messages using the mobile app.