Inheritance-issue a non-Muslim wife:
1) Purchased property in her name during her marriage.
2) She died childless and intestate.
3) Her husband's died long before.
4) She continued with her maiden name, religion, rites and rituals which are non-Muslim.
Kindly explain in the light of the Islamic law who should inherit her property? i) Her relatives from the parental side or ii) Her relatives from the in-laws side.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If this woman died as a non-Muslim, then it is her non-Muslim heirs who were non-Muslims the time of her death, who would inherit her, whether they were from the same religion like her or from another religion, like for instance if she is a Jew and her heir is a Christian, because these religions are alike [do not believe in Islamic Monotheism]; this is the view of the majority of the scholars. Allaah Says (which means): {And those who disbelieve are allies to one another.}[Quran 8:73]. As regards a Muslim, he does not inherit anything from a non-Muslim, whether he is a husband or a relative by family lineage or by marriage, and this is the view of the majority of scholars. The Prophet said: "A Muslim does not inherit a non-Muslim and a non- Muslim does not inherit a Muslim." [Al-Bukhari and Muslim] 

Allaah Knows best.