According to the conditions you have mentioned, and only according to those conditions, you may use plastic hair extensions. The Shafi`i scholars say that using non-human hair is permissible only if it is of a pure substance and the motive behind it (for a woman) is beautify herself for her husband.
Responding to this in detail, we would like to cite the explanation of Sheihk Bakr ibn `Abdullah ibn Abu Zayd, in his book, Fiqh An-Nawazil, (Islam’s Stance on Contemporary Issues):
“In an Islamic perspective, there is a consensus among the scholars that adding artificial hair to one’s hair is generally prohibited. They quote the following as evidence:
Imam Al-Bukhari narrated on the authority of ‘A’ishah (may Allah be pleased with her) that an Ansari girl after marriage got sick and all her hair fell out. Intending to provide her with false hair, they asked the Prophet (peace and blessings be upon him) who said: ‘Allah has cursed the lady who adds artificial hair (to hers or to someone else’s) (al-Wasilah) and also the one who asks for it (al-Mustawsilah)”
Also, Imam Al-Bukhari narrated on the authority of Ibn `Umar (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: ‘Allah has cursed al-Wasilah and al-Mustawsilah and also a lady who tattoos herself or someone else) or gets herself tattooed (i.e. asks for it).’
What does the previous evidence connote?
This evidence indicates that adding false hair to one’s hair is unlawful, because one never incurs Allah’s curse or wrath save on something prohibited. So cursing here stands as strong evidence that a particular act is completely prohibited. Some scholars even consider doing something that incurs curse is tantamount to committing a major sin. Imam an-Nawawi said: ‘The hadith implies that adding false hair is one of the major sins as the person who does it is cursed.’
Moreover, there is unanimity among the scholars of the Hanafi, Maliki, Hanbali, Zahiri and Shafi‘i schools, that it is prohibited for the woman to use artificial human hair with the purpose of beautification. This prohibition applies whether the attached hair is hers, her husband’s, one of her mahrams (a non-marriageable relative) or another woman’s hair as the previous hadiths are general in prohibiting using artificial hair.
However, the Hanafi school of jurisprudence maintains that using non-human hair such as wool, camel hair, goat hair and pieces of cloth is permissible because this does not imply cheating, and because parts of the human body are not used in this case, which is originally the reason for the prohibition in the opinion of the Hanafi school.
Imam al-Laith Ibn Sa`d also said that it is permissible to lengthen the hair artificially with wool, pieces of cloth and similar items which are not human hair.
But the Maliki school, the Zahiri school and Muhammad ibn Jarir at-Tabari are all of the opinion that lengthening the hair with non-human hair such as wool, animal hair and camels fur is unlawful. Imam Malik said: ‘A woman should not lengthen her hair whether she is using hair or otherwise.’
The scholars subscribing to this opinion use the previously mentioned hadiths as their evidence. They also believe that adding false hair reflects a form of cheating and deception indicating that the woman has thick or long hair in addition to it being a way of changing the nature created by Allah.
The Maliki school makes an exception to this. It is that tying the hair with pieces of cloth and colored silk threads, which actually do not resemble hair and thus they are not prohibited as they are not considered as Wasl (adding artificial hair to woman’s hair) which is not the intention.
The Shafi`i School holds the view that if the woman adds non-human hair to her hair, it is either pure or impure. If it is impure, for example, if it is the hair of a dead animal or the hair of an animal whose flesh is prohibited to eat – if the hair is taken while the animal was still alive – then it is prohibited. If the hair is of a pure substance, then the following should be considered:
1. If the woman who adds this hair is not married, then it is also haram.
2. If the woman is married, then there are three opinions:
The first: Wasl is permissible for her only with her husband’s permission. This concerns hair that looks like human hair, whether it is wool or camel hair. As for the colored silk threads and the like which do not resemble human hair, then it is permissible, as it does not reflect any cheating.
The Hanbali school are of the opinion that if the woman uses items other than natural hair just to tie her hair, then it is permissible as it is a case of necessity which she can’t avoid.
If the woman unnecessarily does it, then there are two opinions: 1) it is disliked, and 2) it is prohibited. Ibn Qudamah held the first opinion.”
In conclusion, it’s clear that scholars are unanimous on the impermissibility of using human hair for hair weaving or extension. But as regards non-human hair, it’s controversial. The scholars of Hanafi school of jurisprudence allow it. But the scholars of Maliki and Hanbali schools maintain that it’s permissible as long as it doesn’t resemble human hair.
The Shafi`i scholars say that using non-human hair is permissible only if it is of a pure substance and the motive behind it (for a woman) is beautify herself for her husband.