This page gives details on only one aspect of HP/HPE-related stock. To find all your stock – and verify or estimate your current cost basis – start here: HP/HPE-related stock 

Before Nov 1, 2000, the HP employee stock purchase program was administered by HP's stock transfer agent. When you left the company, the stock stayed at the transfer agent, currently EQ (Equiniti.)

More recently, the stock purchase, option, and incentive programs have been handled by plan administration divisions of brokerage firms -- "NetBenefits" at Fidelity, "MyBenefits" at Merrill, or "StockPlan Connect" at Morgan Stanley. When you left the company any shares you owned were automatically moved from an employer-paid account at the plan administrator to a personal account at their brokerage division. An annual fee is often charged, which can drain a small account. Details of your purchase lots should be preserved. However, if you move the shares to a different brokerage, shares will be moved in a single lot. Some brokers let you correct the records to include lot-by-lot cost basis data.

If you transfer stock out of an account at a transfer agent, administrator, or brokerage, you must obtain a "Medallion Signature Guarantee." https://www.hpalumni.org/StockMedallion

If there is a stock spinoff, the new stock will either be at the spun-off company's Transfer Agent or in your personal Stock Brokerage account – depending on where the parent stock was located.