Marketing Cloud tracks subscriber information for 6 months in its System Data Views. This time range is default (although you can engage support to extend this).
Unfortunately, these tables are read only and do not allow you to migrate / copy customer history into them. To by pass this, you would have to export your customer engagement data into Data Extensions within Marketing Cloud. This is particularly useful for IP warm up and to segment initially. As time goes on, the data from the old system becomes stale and you can rely solely on the info from SFMC.
For integration for website, you might want to look at Predictive Web