Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is permissible to buy and keep stuffed animals or birds, because there is no religious evidence that prohibits this.
2- However, if this leads to the wasteful spending of money, it is considered prohibited due to this reason.
The prominent Muslim scholar Dr. `Abdullah Al-Faqih, supervisor of Fatwa Centre at www.islamweb.net, Qatar, adds:
Islam forbids Muslims to wastefully spend their money, even in permissible and lawful things. Almighty Allah describes the characteristics of true believers and says, “And those who, when they spend, are neither prodigal nor grudging; and there is ever a firm station between the two.” (Al-Furqan 25:67)
Stuffing is a process in which the animal’s skin is treated chemically or in a certain way so as to keep it safe from decay. This is done for the purpose of using the animal or bird either in the pursuit of knowledge or in beautifying the house.
As far as Islam is concerned, this is not haram, for there is no evidence to say so. Drawing a similarity between such things and statues is not correct because they are the exact creation of Allah, not an imitation of it.
However, if this leads to the wasteful spending of money or extravagance, it becomes impermissible for this reason.
The Prophet (peace and blessings be upon him) says, “Allah dislikes for you gossiping, asking too many questions and wasting money.” (Al-Bukhari)
Allah Almighty knows best.