All perfect praise be to Allah, The Lord of the Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
The majority of the Muslim scholars are of the view that, in principle, rights and benefits are received by inheritance. Therefore, persons to whom a bequest is made are entitled to receive all types of the deceased`s wealth: assets, benefits and rights. Al-Ramli said: "As wealth is received by inheritance so are rights." {Hashyat al-Ramli Ala Asna Al-Matalib, 3/3}. However, a bequest shouldn`t exceed one third of the estate since the Prophet (PBUH) said: "One-third, yet even one third is too much." {Related by Bukhari}.
As regards the bequest made to the person in the above question, he isn`t entitled to receive anything from the revenue of the shop since after the death of the testator the right to the Ijarah (Hiring) is moved to the heirs. Therefore, the person to whom the bequest was made isn`t entitled to receive any part of the revenue since the revenue is an outcome of that business (shop), and the testator doesn`t have the right to gift the revenue of his heirs` business. And Allah knows best.