It is not to be considered unconstitutional if a surviving person of a common law marriage is not treated like a spouse or a same-sex registered partner (see also Federal Constitutional Court June 1, 1983, 1 BvR 107/83, Federal Fiscal Gazette 1984, pt. II, p. 172).
Furthermore, the different treatment of a surviving person of a common law marriage and a surviving spouse or same-sex registered partner is not contrary to the free movement of capital (Art. 63 Treaty on the Functioning of the European Union (TFEU)).
For more details regarding the relevant tax class of the acquirer see Koeniger, The German Inheritance and Gift Tax, 2017, p. 243 et seqq.