A dowry is essentially a marital gift that is given to the groom by a bride upon marriage. It is like a promise that the wife will have something to bring to the marriage, some asset that the husband can depend on and depend on her for.
To dream that you inherit a dowry means that you feel like you have achieved a reward for having a change in character or a change in thought. When you get married in a dream this is not to mean that you are married in real life or to signify a change in your relationships usually. This is to signify that you have married two ideas in your mind to create one greater one. If you have a dream in which you inherit a dowry then this means that you are being rewarded because of that thought.
A dowry is something that is given away to the husband as assurance that the wife is worth something. To have a dream in which you are giving away a dowry it means that you are ready to give yourself to someone or to a cause totally. You are ready to strip yourself of your assets and share your resources and skills with whomever it may be that is so important to you in your life. Only you can know who this significant other or organization might be, but whoever it is, they must be very important to you.