Updating one table from another table where non-primary-key field is similar string
Without the primary key, fixing the data with an update statement is likely to get very messy.  You're most likely better off getting a fresh export of the original data with the PK included, run the process/es that you did to clean up the data, then run an update statement.  And then put constraints on the table to prevent the errors from occurring again.

The update statement should be fairly simple though.  I don't know the full syntax for Access, but here's the general SQL statement I'd use on SQL Server:

update TableA
set FieldA = source.FieldA
from TableA destination
inner join TableB source
on destination.PK_ID = source.PK_ID