According to Yourdon & Demarco who’s notation you use, each process should be uniquely numbered and appear in only one of the data flow decomposition diagram. Your second alternative would therefore be wrong, if it is one and the same process.
There is no issue with several external entities receiving data from the same process. So the first alternative seems ok to me. However there is an ambiguity in the diagram about whether both receive the same data at the same time or of it is meant as alternatives. Yourdon & Demarco use a +
symbol in a rounded circle between the two outgoing flows to mean “or” (Figure 24, page 61 in Structured Analysis and Design Specification).
Yourdon & Demarco claim that each data flow should have a unique name. However this seems more a recommendation to me to disambiguate similar flows of different data. I didn’t find equivalent guidance in Gane & Sarson. So I think in your case it would be ok with the . However, if you want to play it by the book, you could consider to use:
- either a single external entity called “academic user" and explain that it can be both a student or a teacher,
- or a slightly different name in the flow if it appears that both types of users look at different kind of boards,
Edit: You may also use a “gyration” (figure 16 page 55 in their book), i.e having a main named arrow from the process to one entity, and let another divergent arrow deviate from the main arrow to the second entity (no name since it’s the same flow). I have however not seen many of those in DFDs neither in their book nor in practice, probably because fewer tools facilitate this style of diverging arrows.