Especially with the Sun, if it is near the next house cusp then it will affect it but it's not technically "in there" as Dear Hs666 put. If also for example, it is on that house cusp, I would not count it as affecting the previous house as much at all.
Example:
Sun in the end of the 1st house might make a solar personality in things more like clothing style, how you characterise yourself with what you own for example (2nd house consequently has somewhat to do with those) but this would not be as strong on the personality as Sun on the Ascendant. It would "shine" into the 2nd house though, giving a Solar position there, and the closer to the cusp the more that is so. Hence things being more 2nd house related.
Sun in the ascendant might not be as concerned with money and possessions necessarily where a later 1st house Sun person, likely will. You can use these as a measure.
In your Example:
A later 8th house Sun would be not as sexually and other 8th house focused, but instead more endeavouring and higher education interests in life are central to them, which is the 9th. Still somewhat. Less occultic 8th house Sun, more philosophical interest in of itself, blending in.
A 9th house university professor might have to delve into secretive stuff for research and struggle more, a late 8th house professor might be naturally better at deep research, into the obfuscated and hidden things involved, but it's not as straightforward an indication for the rest of this professors academic career, as another rough example. Maybe he has diverging interests from other faculty, his divergent interests actually characterize him as a professor (not secretive about it), he is not as naive and world faring as 9th house, is more serious and Scorpio like as an academic. Etc.
This would be only one indicator in itself. You can have this person with 9th house Sun as well if other placements support it.tha
