Unfortunately the information for lead source is not copying over to the account.
I now know that the field name and field type must both match between the modules for this process to work but unfortunately this was not clear to me before.
Since "Lead source" is not a standard field in the accounts module I have created this. This field does not match the field for Lead source in the other modules where it is listed as a standard field (e.g. in Leads).
I assume one way would be to create completely new fields for all necessary modules and then follow the way described in the artile "Converting a DropDown Field to a TextField" to copy data from the "old" dropdown to the "new" one.
I am not sure if this is the best solution.
Already having data in the system what is the easiest way to make that process work?