What address should be included on the invoice?

In the case of a police check, you must have a document confirming the purchase of the drug or a scan of the prescription, and preferably both. If the data on both documents are the same, there is no reason to worry.

It is about security in the context of a possible police check. Is such a document invalid for them, or do the remaining data confirm the right to possess the drug?

It depends for what purposes you need an invoice. As a rule, in the case of natural persons, the address of residence should be on the invoice. As a rule, the pharmacy issues an invoice for the data on the prescription, so in the future you need to change your data in the clinic (at the doctor who issued the prescription). If you need an invoice for settlements with the Tax Office, the address indicated on the invoice must match the address provided in the application to the office. I enclose materials that may be interesting and information about the possibility of using teleconsultation: https://www.gdziepolek.pl/blog/jak-zrealizowac-e-recepte-w-aptece https://www.gdziepolek.pl/blog/w-czym-moze-pomoc-ci-gdziepolek https://www.gdziepolek.pl/telekonsultacja