From the docs:
When you convert a lead, data in standard lead fields is transferred
into standard account, contact, and opportunity fields. For custom
lead fields, the data is mapped to custom account, contact, and
opportunity fields as specified by your administrator.
Currently we can only map custom Lead fields with custom fields on
Accounts, Contacts or Opportunities objects.
If you want to map a Standard Lead field to a custom field on Accounts
or Contacts or Opportunities object, follow below given steps.
For Example: How to map standard Rating field on lead record to custom
field on Contact object?
Step 1: Click on Setup | Customize | Leads | Fields | Click the "New"
button | select Data Type: Formula | Return Type: Text Formula:
Text(Rating) | Save it. This custom field in Leads will get the value
from the standard field.
Step 2: Click on Setup | Customize | Contacts | Fields | Click the
"New" button | select Data Type: Text We are creating a field in
contact object with same data type as the field on lead.
Step 3: Click on Setup | Customize | Leads | Fields Click the Map Lead
Fields button | Map: Custom formula "Rating field" from step 1 to
custom Contact object "Rating field" from step 2 and click Save. With
the above steps we can pass value from standard Lead field to custom
field on Contact object.
The same can be done for account and opportunity objects too