No. When S sails on past the lay line she has overstood the windward mark and therefore is no longer on a beat to windward. Rule 18.2(b) is written to cover exactly the situation where one of the boats has overstood and therefore is no longer close hauled. The Case is 100% correct.

I do not think so.
The diagram in Case 9 shows 2 boats on opposite tacks and the proper course for one of them, but not both, is to tack and that is exactly what rule 18.1 b) refers.

My guess:

18.1 (a) is really a specialized version of exception 18.1(b).  The exception of 18.1(a) only applies if the boats are beating while 18.1(b) applies if they are beating or reaching.  They reference 18.1(b) because it is the more generalized exception.  The authors didn’t want readers to think that the findings were only valid if the boats were beating. 

No, the proper course for S is to tack to round the mark and P will not need to tack.

The reference in 18.1 (a) depends on the course that the boats are actually sailing and not the leg of the course being sailed. If the wind shifts, one might be on a beat to windward at a different mark, or one boat may be reaching in on one tack rather than sailing close hauled to the "windward" mark.

I´m Spanish and usually don’t speak English, so is possible for me to have problems with English language and rules translation.

Rule 18.1 says that 18.1 don´t apply …(a) between boats on opposite tacks on a beat to windward, and (b) between boats on opposite tacks when the proper course at the mark for one but not both of them is to tack,…

I understand that the differences among both rules rely in the course of the boats, as they have the same purpose. Dick Rose explains it very well in “sailing world.com”

First sentence in Case 9 talks about “Two close-hauled boats on opposite tacks …” but in the picture P has passed the layline, although her course seems to be close-hauled. This is not the course that would make her arrive as soon as possible to the mark.

Case 132 says: “A boat is ‘on a beat to windward’ when the course she would sail to finish as soon as possible in the absence of all other boats is a close-hauled course or above” and “for the purposes of rules 18.1(a) and 42.3(c), a boat is on a beat to windward when the course she would sail to finish as soon as possible in the absence of all other boats is a close-hauled course or above”.

Perhaps this is the reason for my misunderstanding.

From a practical point of view, being 18.1(a) or (b) the rule that apply, the consequences are the same.

Thank you very much for your opinions.

I´m Spanish and usually don’t speak English, so is possible for me to have problems with English language and rules translation.

Rule 18.1 says that 18.1 don´t apply …(a) between boats on opposite tacks on a beat to windward, and (b) between boats on opposite tacks when the proper course at the mark for one but not both of them is to tack,…

I understand de differences among both rules lies in the course of the boats, as the have the same intention. Dick Rose explains it very well in “sailing world.com”

First sentence in Case 9 talks about “Two close-hauled boats on opposite tacks …” but in the picture P has passed the layline, although her course seems to be close-hauled. This is not the course that would make her arrive as soon as possible to the mark.

Case 132 says: “A boat is ‘on a beat to windward’ when the course she would sail to finish as soon as possible in the absence of all other boats is a close-hauled course or above” and “for the purposes of rules 18.1(a) and 42.3(c), a boat is on a beat to windward when the course she would sail to finish as soon as possible in the absence of all other boats is a close-hauled course or above”.

Perhaps this is the reason for my misunderstanding.

From a practical point of view, being 18.1(a) or (b) the rule that apply, the consequences are the same.

Thank you very much for your opinions.

Use of the term proper course in Rule 18.1(b) may be misleading.  Although a proper course for S would involve a tack, no Rule compels her to sail a proper course in this situation.