All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the deceased did not leave any other heirs except those mentioned, then his wife gets one-fourth as her legal share due to the non-existence of children (direct heirs); Allaah says (what means): {And for them [i.e. the wives] is one fourth if you leave no child..} [Quran 4:12]
The remainder should be divided among his full-brother and his full-sisters by Ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male is entitled to twice the share of the female, as Allaah says (what means): {If there are both brothers and sisters, the male will have the share of two females.}[Quran 4:176]
The two sons of the brother do not get any part of the inheritance because they are prevented by the existence of the brother.
Therefore, the inheritance should be divided into 8 shares, the wife gets one-fourth, which is 2 shares, his full brother gets 2 shares, and each full sister gets 1 share.
As regards what you mentioned about the will which the deceased had made, then you should first know that life insurance is forbidden, and if a person dies it is not permissible for his heirs to take any of the insurance money except what he has paid to the insurance company. So, what the deceased legitimately possessed and can be inherited is what he had originally paid to the insurance company, and it belongs to all of the heirs because it is part of the inheritance.
With regard to his bequest to his wife, whether it is the insurance or the retirement pension - if this is something that can be inherited – then the bequest should not be executed because it is a bequest to an heir and it cannot be executed without the consent of all of the heirs. Abu Umaamah Al-Baahili said: “I heard the Messenger of Allaah say: 'Verily Allaah has given every rightful person his right, so there is no will for an heir.' This was presented in the Hadeeth collections of Ahmad, Abu Daawood and At-Tirmithi, and Al-Albaani classified it as Saheeh (authentic). Also, Ad-Daaraqutni reported it as being related by Ibn ‘Abbaas but there is an addition in the end of it: 'Unless the heirs agree to this'. Its Isnaad (chain of transmission) is considered acceptable.
Also, if the retirement pension is dues of the deceased from his employer, then it is part of the inheritance and it should be divided among the heirs. The deceased's bequest to his wife as associated with any part of this pension is not effective except after the consent of all heirs, as we have already clarified. In case the retirement pension is a donation from the government, then it is not part of the inheritance and it should be given to those designated by the government. For more benefit, please refer to Fatwas 81441 and 85811.
Regarding his bequest to the person he adopted, the bequest is valid, but since the deceased combined a bequest for an heir – his wife – and a bequest to a non-heir – the adopted person, then the statements of the scholars in regard to whoever bequests something to an heir and a non-heir apply to his will, and it is of two cases:
1- If the amount of the bequest does not exceed one-third of the estate, then if all the heirs approve of the bequest to the wife, then the bequested sum is to be divided equally between her and the adopted person. In case the heirs refuse the bequest to the wife, then the adopted person is entitled to half of the bequested sum, and the other half is to be added to the total inheritance.
2- If the amount of the bequest exceeds one-third of the estate, then if all the heirs approve of the entire bequest, then the will should be divided between her and the adopted person. If the heirs refuse a bequest greater than one-third, without refusing the bequest to the wife, then a third should be divided between the wife and the adopted person. If the heirs refuse the bequest to the wife, then the adopted person takes the entire third. Mataalib Uli An-Nuha reads: “If [the deceased] bequests one-third, i.e. one-third of the estate, to both an heir and a non-heir, and all the heirs approve of the bequest to the heir, then the bequested sum should be divided between them equally [half-and-half]; and if he bequests two-thirds to them equally, and the heirs refuse half of the bequest (which exceeds one-third) ... then the one-third is to be divided between them because the heir is entitled to the bequest with the non-heir when the heirs approve of the bequest; so if they refuse it, then it is an obligation that the remainder be divided between them. Al-Qaadhi mentioned this. But if the heirs refuse the share of an heir only, or they approved of the bequest to a non-heir only, then he [the non-heir] gets the entire one-third.”
For more benefit, please refer to Fataawa 119119 and 82371.
Allaah Knows best.