Remote query (openquery) to linked server fails after upgrading to SQL Server 2016
The query you're sending to the linked server (via OPENQUERY) shouldn't also contain its own reference to the linked server (via 4-part name), unless the linked server has its own loopback linked server with the same linked server name (and even if it does, I wouldn't try to stack linked servers like that). Try:

SELECT t.Name, t.Disabled
FROM OPENQUERY
(
   [Linked_Server], 
   N'select t.Name, t.Disabled 
     from [Database-1A].[dbo].[My_tbl] AS t 
     where t.ID=232627;'
) AS t;