Directly copying just the workoutsDB.db to the appropriate place on the new phone, after Strong Log has been installed and launched once worked for me. (On a Moto Razr Maxx)
I tried it a few other ways without luck, but their dev emailed me these specific steps and it did the trick:
1. copy the original workoutsDB.db file somewhere
2. install Stong Log on the new device
3. open Strong Log (the schema for the database is created on initial opening of the app)
4. close app.
5. find the new workoutsDB.db file and delete it.
6. add the old workoutsDB.db and reopen the app.
Couple of notes:
A. On my phone the workoutsDB.db file lives in /data/data/com.driftwood.workouts/databases/. You need root to read and write to the /data directory.
B. The only file I replaced was the workoutsDB.db file. I left the workoutsDB.db-journal file, and the rest of the files that are created on first launch as they were after the first-launch.
C. I killed the Strong Log app after doing the first-launch of Strong Log and before replacing the workoutsDB.db. (May not matter but seemed safer to me.)
D. When you re-open Strong Log, it will still ask you for your birthday, but it makes sense that birthday wouldn't be part of the workoutDB. Once you get past the birthday screen, your old workouts are all there.
Go get strong! (And remember how strong you used to be!)