Backup and restore SMS and call history

How do you backup and restore SMS and call history with GrapheneOS?

I would like to have a process that works if I loose my phone or want to transfer to new phone.

PS: I don't want to backup the whole phone so cannot use Seedvault.

Agreed on sms-ie! Was able to consolidate complete SMS+MMS history from two old phones into my new Graphene'd Pixel.

No hiccups. Just worked.

Sideloading the APK for fetching old phones' data, via USB, is supposedly possible down to Android 4.4.

Keep it around for backups (can be scheduled) on my current device as well.

Can only recommend.

Is there any native way to backup similar to the export feature in the Contacts app?

hello-gos SeedVault backup works to backup & restore SMS, but doesn't backup call history.