If you are not very familiar with Recorder, you could just ask the LRC to export your records back to you as GIS layer or Access database or spreadsheet (depending on the number of records involved).

To do it yourself you could use the report wizard - http://jncc.defra.gov.uk/page-4852. To get all your records don't use any restrict to options on the first window and tick "include all taxa" on the second window.  Do you have any confidential records etc? If so you'll need to change the defaults to export those as well in the "additional filters" bit, and include fields for them (so you can see later which were unverified, marked as confidential, zero abundance). Tick all the fields you've ever used. The number of records returned should be the same as the number of species observations on the welcome window.

Then export to your required format - there is some information here: http://jncc.defra.gov.uk/page-4853. The report wizard can export to a GIS shapefile (the fields will be attributes), an excel spreadsheet and an access database amongst others.

There are some fields that the report wizard doesn't report on, so you'll lose that information (e.g. spatial reference qualifier). Someone more technical than me might have a way to keep that information archived - or you could just keep the R6 db sitting there quietly in case you need to go back to it? (e.g. We still go back to Recorder 3 occasionally as not quite everything was migrated to Recorder 6!)