"Leaflet on the choice of tax class for the year 2023 for spouses or civil partners who are both employees" facilitates the choice of tax class and provides further information (including on the factor method).
(updated version - as of 14.02.2023)
In the future, employees who are only subject to limited income tax liability in Germany will also be assigned a tax identification number (sections 39(3), 42b(1) sentence 1 EStG).
This assignment is to be made by the employee at the employer's permanent establishment tax office.
However, employees are to be given the option of authorizing their employer to apply for the tax ID for the first time. Then the notification letter from the tax administration will be sent directly to the employer.
Since 01.01.2020, employees with limited income tax liability have been included in the annual company income tax equalization.