iMessages on laptop don't sync

Usually if all other settings appear OK, those in Continuity may need attention, to allow a connection.

• Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support

https://support.apple.com/en-us/HT204681

Several items are covered in the above article; and some overlap, even though seemingly dissimilar.

Also restart the iOS device and the Mac afterword to test. The answer should be among settings.

The link through ASC (support communities) has one URL to a good support article.

I'm following some of my threads in discussions and see those in my email.

• Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support

https://support.apple.com/en-us/HT204681

Have you tried the main link above and read through to see which ones apply?

I've used this information to successfully resolve issues with my Mac & iPhone.

As stated, certain aspects of 'continuity' can be set and functional change made there.

Among those, other links to content in each part are available with more information.

An example of this, which had an affect on other Continuity features, appears within:

• How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

https://support.apple.com/en-us/HT208386

For other aspects of Messages/iCould (that may or not affect your continuity) see detail here:

Learn how to keep all your messages in iCloud.

Learn more about Messages.

• Wireless carrier support and features for iPhone in the United States and Canada - Apple Support

https://support.apple.com/en-us/HT204039

(shows what should be available, from service provider, for each feature set)