Set a LookUp field of "Account Name" in "Lead" Stage and preserve the Account asociation when converting to a "Contact"

Set a LookUp field of "Account Name" in "Lead" Stage and preserve the Account asociation when converting to a "Contact"

AS IS:
  1. When creating a new lead user is prompted to set Company field and Account field
  2. When converting a Lead to a Contact, the Company name is used to create a brand new Account
In our use case, we need to set Account field during the Lead process and then asociate it to an Account later on, is it possible to create the following relation of fields?

Custom Lookup field for Accounts in Lead layout -> Auto populates Account Name Lookup Field in Contact layout