There is one more thing we can do to figure it out.
In The Netherlands we have the so-called register of inhabitants. This is a register where all the inhabitants (incl. date and place of birth) are listed over periods of 10 years. And most important, it also lists all the movements of the inhabitants, when and from where they came in the town and when and where to they left.
If Johanna M is the Anna who left for the USA in 1873, it will be noted there. If she returned, also, And if she is the Johanna who left in 1884, it will also be noted there.
Just one problem; not all towns/cities have these registers online. Haarlem is one of them.
I will phone the archives where they keep the registers of Haarlem on tuesday, the first day they are open again.
That is, if I have the time. Half July I have been diagnosed with a lower back hernia, and monday I have an appointment with the neurosurgeon. I will most probably get surgery. The date of that surgery I will find out on monday as well as the date of the examination by the anesthesist a few days prior to the surgery.
Below you will find the link (in English) to the archives where the registrations of inhabitants of Haarlem are stored.