There are multiple searches that make use of the Lead Conversion Date Filter, such as Creating a saved search that shows Lead Conversion progression.
When creating a Saved Search for Clients/Customers, under the Originating Lead Fields... there are scenarios where this field is not available.
The Conversion date will not be available unless the Lead Conversion feature is enabled.
1. Navigate to Setup > Company > Enable Features.
2. Under CRM Tab > Sales.
3. Mark the Lead Conversion checkbox.
4. Click Save.