The trouble with using the Export function is that it only exports the data showing on the screen, not all customer information. I presume this post is related to your other question about deleting sales invoices. You are probably thinking to import the entire old business to get the customer list, but delete the accounting data. That may be your only choice for now.
This topic has come up before. See Exporting customer list to spreadsheet - #7 by Siddharth. Custom reports feature is still a work in progress. So I think there is no easy answer, but you may be able to figure something out via custom reports. That is beyond my skill level.