Following steps must be taken before/during the HLR migration:
1. Database backup for modification of data if this is an inter-vendor HLR migration.
2. Provisioning embargo for data consistency.
3. Database dump after the embargo
4. Data modification according to the new HLR DB format
5. Routing of SCCP messages from signalling gateway (STP in many cases these days) to the new HLR2
6. Reduction in BSS/RAN LU timer
7. Necessary testings and their verification from charging perspective.
I think your query of sending SAI to new HLR will be addressed in point no. 5
I hope it helps you out.