Yesterday, Windows installed updates:
KB5032292 Monthly Rollup for Windows 7 - successfully installed
KB890830 Malicious Software Removal Tool - failure with error 0x8024001E
Even if the message is "failure", I think everything is fine. In fact, the MSRT has been launched (the latest version) and has scanned the computer.
Below the following log: C:\Windows\Debug\mrt.log
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Microsoft Windows Malicious Software Removal Tool v5.73, June 2019 (build 5.73.16044.1)
Started On Wed Jun 12 10:58:03 2019
Engine: 1.1.15900.4
Signatures: 1.293.2420.0
MpGear: 1.1.15747.1
Run Mode: Scan Run From Windows Update
Results Summary:
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No infection found.
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Today (as every day), Windows Update searched for available updates, with the result "no updates available".
So Windows Update works correctly, Avast as well, and I'm sure the reported problem is solved.
Thank you again for your help.