When adding/changing fields that are converted from Leads to Accounts/Contacts/Deals, you can use the Lead Conversion Mapping menu to ensure fields are copied over.
You can select different mapping per Layout, then using the drop-down menus you can select which fields in Accounts/Contacts/Deals each Leads field will be copied to when converting:

Ensure the data type of each field is the same as the one it needs to be mapped to.
E.g. if you need a number copied over from Leads to Account, make sure it is of data type 'number' in both modules.