The decline of her morale was fascinating.
The decline in her morale was fascinating.
Which one is correct? Additionally please tell me if the use of 'in' or 'of' after 'decline' is a use of appropriate preposition or contextual-based.
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It is difficult to provide a rule that will always tell you which is correct, because you will probably find exceptions to that rule. You can find many examples of both usages without too much trouble, although it is reasonable to say the 'decline in' is the most commonly used phrase.
As a very general guide:
There has been a decline in the percentage of voters who agree with the proposition.
There has been a decline in the quality of wool coming from areas affected by drought.
There has been a decline of five percent in the percentage of voters who agree with the proposition.
The Decline and Fall of the Roman Empire.
The decline of the print industry since the internet became popular.
The decline of Blockbuster because of its failure to innovate.
Just for completeness, 'decline' does not have to be followed by 'in' or 'of', e.g.:
The Roman empire's decline was brought about by...
Standards have been in decline for years.
He died following a long period of decline.
The last two sentences still use 'in' and 'of' but they appear before 'decline'.
Of the two sentences that you asked about, I think that either could be used, but the second sounds better to me.
Check dictionaries. It says decline in is the usage. One such entry is here on Collins.
If there is a decline in something, it becomes less in quantity, importance, or quality.
On the other hand, we also have many books with titles including decline of something here.
In short, both are okay but in the context you asked, 'in' goes better.
BTW, I'm not sure why it would be fascinating if there's a decline in morale!