simple pst or past perfect

Here is a sentence I am not sure which tense is right:

A 32-year-old woman died in a hospital last night after she fell from a 250-foot cliff.
or
A 32-year-old woman died in a hospital last night after she had fallen from a 250-foot cliff.

The past perfect in the second sentence follows the rule that the earlier action of falling happened before the death but it would be acceptable to use ‘fell’ because ‘after’ already indicates the sequence of events.

Yes, words like after, before, already etc make the time of occurrence appeal more quickly to the listener or the reader. However, if we use a conjunction like ‘because’, ‘since’ or ‘as’, the first sentence would invariably require the past perfect tense. I hope Alan will agree with me.

Thank you both Alan and Anglophile for your help.

Hersheysoldier