This is not related to the broken Messages app.
After I formatted my drive, installed clean El Capitan and received a code on my iPhone I can send iMessages from my Mac. Messages are received by my contacts and I can also see them on my phone.
The problem is that I would like to see all existing (previous) messages I have on my phone, again in my Messages.app. That is, everything I wrote before formatting the drive.
I haven't made any backups. I thought that simply everything will be synchronised like Contacts etc.
Currently only newly created messages are visible. Since yesterday, I've been reading a bunch of topics. Is this normal? Or am I missing something? As I said, it doesn't look like a sync issue since the new messages are working.