Updating new securities transferred-in-kind from an outside brokerage to my Charles Schwab account?

I think what you're seeing there is an "alert" from the National Financial Alert system, a communication protocol for financial institutions.  You shouldn't be seeing that so I expect it's an artifact (problem) associated with the recent decision by Schwab to move to EWC for downloading.

Personally I'd first go into that "from" Account in Quicken and use the "Shares Transferred Between Accounts" action to move the securities from that Account to Schwab.  In the best of times these sorts of actions aren't properly handled by many financial institutions, and these aren't the best of times right now.

For each security you select you should see one Remove action for that security in the "from" Account and multiple Add actions (one for each lot) in the "to" Account. 

If it happens that your "from" financial institution and Schwab get it right then the download, when it happens, (EWC typically only polls once a day at night), should result in a bunch of "Match" transactions that you can accept.  If you get something else downloaded to you, simply delete those downloads.

Are the new securities actually in your real-world Schwab account at this point, but still no download of the securities from Schwab into Quicken at this point?

If the answer is "Yes" then some sort of manual entry on your part will be required.  The simplest approach here is to do one Add action for each security as any old "lot" information has gone away.  Unless the executor of the estate used the alternative "6 months after death" valuation you'd use the securities' closing price at date of death as your cost basis.  (The "step up" in valuation.)  The securities are considered "long term" holdings irrespective of how long the donor or you actually owned the stock, so use a Date acquired of 1 year before date of death.