Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is unlawful for the woman to lengthen her hair with any natural or superficial hair. Doing so is even a major sin. In a sound Hadith, the Prophet said: "Allah has cursed the Wasilah and the Mustawsilah". Wasilah is the one whose profession is making wigs and hair pieces. Mustawsilah is the one who uses them.
Ahmad reported from Hamid Ibn Abdurrahman that he said: "I saw Muawiya giving a sermon on the Minbar and he had a handful of (long) hair. I heard him saying! "Where are your scholars, O people of Medina? I heard the Prophet forbidding anything like this and he (the Prophet) said: "Indeed, the children of Israel have been punished - destroyed in another narration - when their women got used to using these".
But lengthening it with something other than hair is permissible like using Qaramil (use of wool or silk to make braids). Ibn Qudama says: "If what she uses does not exceed the minimum necessary to tighten up her braids there is no harm in it as it can not be avoided to use it".
This is similar to what Shaikh Qardawi said in the book mentioned. I quote from it:
"What is forbidden as far as the woman's beautification is concerned is to lengthen her hair with any other hair; natural or synthetic like what is known now as Barouka….". then he added: "But if the woman lengthens her hair with some threads, some tissue and the like, this is not included in the prohibition. Said Ibn Jubair said: "There is no harm in using Qaramil". Qaramil are threads of silk or wool used as braids which women use to lengthen their hair. Imam Ahmad also allowed this.
Allah knows best.