ID relation between lead and contact

ID relation between lead and contact

Issue : I use API to insert lead and API returns me lead ID which I store in my system. In the moment when I convert lead to contact the ID of the contact is different.
Question: probably I have to store some additional ID (which is the same for lead and contact) on my system? Because after conversion if i'll try to find lead by ID system will tell me that there is no such lead and my system will create new lead (which in fact will be duplicate of contact)