@hans1977se Thanks ! I expected this to be automated
Copying databases for the contacts worked, but for the SMS the message application starts but seems to perform the DB migration for some seconds (maybe 30 seconds) then displays a screen "send your first message".
I think it is due to some timeout for the DB migration. The statement "update text_events set informationType=0;" took 2 or 3 minutes to complete on my telephone (I have a big amount of SMS / MMS). Maybe the automated DB migration works when you just have a small amount of messages ...

Hi !
I just manage to migrate my history.sqlite file from my BQ aquarius 4.5 (with latest ubuntu touch updates) to my Nexus 5 (with a fresh ubport install).
The "old" database is in version 12, the new one is in version 17. So some modifications must be applied.
In my case my fresh install IS fresh (I do not have any previous message on it => I drop tables)

BEFORE: make a copy of the original/old history AND a copy of the fresh installed history: thoose are located in ~/.local/share/history-service/ on each phone. If you don't know / success to make a copy please do not go further.

WARNING: this process will destroy any message on the "new" phone.

I think its OK for the legal warnings

Let's suppose we are on the new phone and we have copied the "old" database on the new phone in ~/.local/share/history-service_old/ (including attachements of course ;).

First, let update the database structure of the old DB:

sqlite3 ~/.local/share/history-service_old/history.sqlite
sqlite> update schema_version set version=17;
sqlite> ALTER TABLE threads ADD COLUMN chatType tinyint;
sqlite> update threads set chatType=1;
sqlite> ALTER TABLE thread_participants ADD COLUMN alias varchar(255);
sqlite> ALTER TABLE thread_participants ADD COLUMN state tinyint;
sqlite> ALTER TABLE thread_participants ADD COLUMN roles tinyint;
sqlite> update thread_participants set state=0;
sqlite> update thread_participants set roles=0;
sqlite> ALTER TABLE text_events ADD COLUMN informationType integer;
sqlite> update text_events set informationType=0;
Exit with "Ctrl+D"

This last "update" will take some time depending on the number of messages you have ...

Now dump the data to an SQL file:

sqlite3 ~/.local/share/history-service_old/history.sqlite .dump > history.sqlite_old.sql

Now let's clean the current ("fresh") database:

sqlite3 ~/.local/share/history-service/history.sqlite
sqlite> drop table threads;
sqlite> drop table thread_participants;
sqlite> drop table voice_events;
sqlite> drop table text_event_attachments;
sqlite> drop table text_events;
Exit with "Ctrl+D"

Now let's insert thoose old data:

sqlite3 ~/.local/share/history-service/history.sqlite < history.sqlite_old.sql
mkdir -p ~/.local/share/history-service/attachments/
rsync -av ~/.local/share/history-service_old/attachments/ ~/.local/share/history-service/attachments/

At last:

sudo reboot

Hope this will help ... It worked for me