All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
If what is meant by the adoption by the couple is just keeping the girl with them for taking care of her and nurturing her without giving her their family name, then this is permissible, but the adoption in which the child is attributed to other than their biological parents is invalid and forbidden, and it does not entail inheritance or being forbidden for marriage.
For more benefit, please refer to fatwas 84422 and 82371.
If the couple want to make the girl possess their house after their death, then they may make a will to her to this effect, and this will is valid for the entire house if it does not exceed one third of the estate. If it exceeds one third of the estate, then the will is not effective in more than one third unless all the heirs approve it, if there are any heirs after their death.
Allah knows best.