Case with exists with innerjoin in update query

Here is some sample data from 2 tables I have

Table 1  
MailCustomer

CustomerID
12345
56768


Table 2
CustomerOrder

CustomerID     MailFlag
12345
66666

I am trying to write an update query that will :

update the Customer flag to 'T' on Customer Order table If the Customer Number exists in the Mail Customer table.  

update the Customer flag to 'F' on Customer Order table If the Customer Number does not exist in the Mail Customer table.  

Given data above table below should look like below after query

CustomerOrder

CustomerID     MailFlag
12345                T
66666                F


Was thinking of using case with inner join but not sure how