Attention to Yeshiva guys, kollel chaps and anybody who wants to listen:
ר' אלחנן in קובץ שיעורים is מדייק a רש"י כתובות לח עמוד ב that a the קנס of מפותה goes to a son. It is apparent that it means דווקא a son, not any other relative. ר' אלחנן and the כלי חמדה among various other אחרונים explain that there are two types of ירושה. One of them is the normal inheritance - that a relative receives. The other is that a son has a special added type of inheritance: He stands in the place of his father. He is קם תחתיו and 'takes over' his father. So even though normally קנס doesn't go via inheritance, to a son it does.
There are a few נפקא מינאs - a גר who has no יורש except for an עובר, even according to the opinion that אין ירושה לעובר, he agrees that to the son it will go once he is born, because he is once again ממלא מקום אביו.
[See משך חכמה that by a mother, both son and daughter are equal, and ר' אברהם גורביץ in ענפי ארז uses this reason to explain that the special inheritance to a son is a link from FATHER--SON, not any other way. Therefore by a mother, both sons and daughters are equal.]
The רמבם writes that ירושה של שררה - of positions [such as כהן גדול, מלך or ראש ישיבה] goes only to a son. Other opinions state that any יורש.
It sounds like this is the מחלוקת - if the ירושה of positions is only for a son who simply takes over his father or actually inheritance.
[The תשובות הרשב"א says by a story of a חזן who lost his voice and wanted his son to take over, his son could. Some say that only a son but other relatives not - which is a חידוש that קם תחתיו while alive still works, whereas other ירושה doesn't.
There is a מחלוקת between the חת"ס and אבני נזר as to whether שררה של תורה goes via inheritance or not in a case where the son is not ממלא מקום אביו - he is not the same in stature as his father, whether it goes to anybody else or another יורש.
[See כתובות ק"ג and רמבם הל' מלכים, and כסף משנה שם.]
מדרש תנחומה brings this week that משה said: Now that the בנות צלפחד one their דין, i will ask ה for my sons to inherit my position.
To answer the obvious questions - משה knew that his sons weren't the same as him, like it says לא קם בישראל כמשה עוד. But he thought they were good enough to get the position [LIKE כתובות ק"ג where ר"ג became נשיא even though he wasn't as good as his father, רבי, but there is no doubt he was eligible to be called נשיא], and thought that even though the sons won't get it because of the second type of inheritance, they can at least get it because of ירושה like any daughter would have got!! Therefore only after the story of בנות צלפחד could משה ask that his sons take over him.
[As to why 'ה refused, there could be many reasons; see the תורת כהנים that they weren't רואי, because they didn't learn. Not to be confused with not being ממלא מקום אבותיו which was physically impossible because of משה's greatness, as mentioned above.]
כך שמעתי ממורי ז"ל, and to protect anonymity i cannot say his name.