Pai Memberships Pro Import OK but no membership assigned

I have created a csv file with the following information:

user_login,user_email,first_name,last_name,display_name,role,membership_id,membership_initial_payment,membership_billing_amount,membership_cycle_number,membership_cycle_period,membership_status,membership_startdate,membership_enddate 

The CSV plugin does not show any error messages and claims the import was OK. But when I check the user in WordPress -> All Users there is no membership level assigned. Also under members in PMPRO the transaction does not appear.

The only data that’s imported is the name,email,username and userrole. I am using PMPRO and their suggested CSV Import plugin.

What am I doing wrong?