You must keep each stock brokerage and administrator up-to-date with your current postal and email addresses.  Your current or former employer does not handle employee-stock-related address changes.

You must make direct contact with each brokerage and administrator at least once a year. Otherwise, depending on state laws and the brokerage or administrator's policies, members report that your stock may be turned over to a state as unclaimed property -- which can be very difficult to retrieve. Checking your statements online doesn't count.

Given the large number of financial companies involved in employee stock -- which change from time to time and may not have passed along the date and cost basis information for each of our stock lots -- you must preserve your own copies of your records.

At some point, you may want to sell some stock -- which could include shares in HP, HPE, Agilent, Keysight, DXC, Perspecta... The brokerage will use the cost basis in their records (which may be $0) to report your apparent profit to the IRS. You could pay taxes twice on the same income!

Easy to check for lost stock and uncashed checks: https://www.hpalumni.org/Unclaimed