yes, muslims don't believe on re-birth. I think re-birth and soul are different.

Islam
Further information: Nafs

There is a hadith reported by Abd Allah ibn Mas'ud, in which it is stated that the soul is put into the human embryo 40 days after fertilization takes place. This version of hadith is supported by some other hadiths narrated by Sahih al-Bukhari and Sahih Al Muslim.

The hadith is as follows: "Verily the creation of every one of you is brought together in the mother's womb as a drop of semen for forty days, then it becomes a clot for the same period, then it becomes a blob of flesh for the same period. Then the angel will be sent unto it to blow into it a SPIRIT, and the angel is ordered (to carry out) with four instructions, to write down its livelihood, the span of life, its deeds, and whether it is wretched or fortunate."

According to the Quran, Ruh (Soul) is a command from Allah (God).

"They put questions to you concerning the Spirit. Say the Spirit is at my Lord's command. ..and of knowledge only a meagre part has been imparted to you." (Qur'an 17:85)
http://en.wikipedia.org/wiki/Soul#Islam
before i meant that may her soul rest in heaven. I'm not a native English so i took both words soul and spirit as one. After death, spirit departs from earth forever.