Is it permissible in Sharia for a partner to undertake additional work related to the primary business without an agreement on the division of its profits? And is the other partner entitled to claim a share of these accumulated profits over 15 years? And what is the share of the heirs from this work?

It appears that the agreement between you, your friend, and your son regarding profit distribution pertains only to the hangar business. Any additional commercial activity undertaken by your son thereafter is not included in this contract. Therefore, you have no right to his profits, except for what relates to the use of your commercial name. You are entitled to financial compensation for its use, the value of which will be determined by the Sharia court and experts for the duration of fifteen years. As for the share of your heirs, it relates to what you owned during your lifetime, such as the commercial name and your share from the hangar business.