A person left a bequest for Haj to be performed on his behalf, after death, when the will was being executed it was found that Haj was more than 1/3 of that persons wealth. will that person be regarded as sinful?
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
If Hajj became fardh (compulsory) on the deceased this year and he had made intention to perform it but he passed away before he could perform it and it was not fardh on him before this year, he will not be sinful for not performing the Hajj because he did not get the time to perform it. However, if Hajj was fardh on him before this year and he delayed it and now passed away, he will be sinful because of not performing Hajj. In this case, it was wājib (obligatory) for him to leave a bequest for Hajj to be performed on his behalf.
If he did leave a bequest (wasiyyat), it will be fardh on the inheritors to implement this if the cost of Hajj can be fulfilled from 1/3 of the inheritance. If the 1/3 of the inheritance is not enough for Hajj, the inheritors can- if they wish- pay for the surplus from their side. (It should be kept in mind that money cannot be taken from a non-mature (ghair-bāligh). If the inheritors don’t agree to do this then they should send someone to do Hajj from such a location where the 1/3 would be enough for Hajj.
If the deceased did not leave a bequest there will be no obligation on the inheritors to perform Hajj on his behalf. However, if they decide to pay for it from their own money (albeit from what they received in the inheritance), the deceased will get the reward. 
It should be kept in mind that the amount of money to be taken out for Hajj-e-badal is the minimum amount. This means that the Hajj should be Hajj-e-Ifrād and Umrah, Qirān and Tamattu’ should not be performed unless the person who gave the order of Hajj-e-badal permitted it. Also, it should be kept in mind that the default ruling for Hajj-e-badal is that it has to be performed by a person who is in the same place as him. If there is not enough money to perform Hajj from the country of the deceased, one may pay someone closer to the Haram to do the Hajj-e-badal. In this case they must ensure that the person that is being ordered to perform the Hajj-e-badal is only doing it on behalf of one person.
If there is not enough money left for even this, then the deceased will be sinful for not performing Hajj.
The inheritors may in this case pay and organise for a Hajj-e-badal to be performed on behalf of the deceased and Inshā-allah, the person will be alleviated of the sin. Finally, it should be kept in mind that most of the costs of the Hajj have to be incurred by the person who gave the order for the Hajj to be valid.
And Allah Ta’āla Knows Best
Checked and Approved by,
Mufti Husain Kadodia
 فتاوى محمودية, ج.١٥, ص.٤٥١, مكتبه محمودية
 خَرَجَ الْمُكَلَّفُ (إلَى الْحَجِّ وَمَاتَ فِي الطَّرِيقِ وَأَوْصَى بِالْحَجِّ عَنْهُ) إنَّمَا تَجِبُ الْوَصِيَّةُ بِهِ إذَا أَخَّرَهُ بَعْدَ وُجُوبِهِ، أَمَّا لَوْ حَجَّ مِنْ عَامِهِ فَلَا (فَإِنْ فُسِّرَ الْمَالُ) أَوْ الْمَكَانُ...
الدر المختار, ص.١٧٣, دار الكتب العلمية
 جواهر الفقه, ج.٤, ص.٢٠٩
 فتاوى محمودية, ج.١٥, ص.٤٤٥, مكتبه محمودية
 فَإِنْ لم يُبَيِّنْ مَكَانًا يَحُجُّ عنه من وَطَنِهِ عِنْدَ عُلَمَائِنَا وَهَذَا إذَا كان ثُلُثُ مَالِهِ يَكْفِي لِلْحَجِّ من وَطَنِهِ فَأَمَّا إذَا كان لَا يَكْفِي لِذَلِكَ فإنه يَحُجُّ عنه من حَيْثُ يُمْكِنُ الْإِحْجَاجُ عنه بِثُلُثِ مَالِهِ كَذَا في الْمُحِيطِ
الفتاوي الهندية, ص.٢٨٥, ج.١, دار الكتب العلمية
 جواهر الفقه, ج.٤, ص.٢١٣