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This question and answer shows the difference between "must have" and "should have" in the past.

They must have told the Police

They should have told the Police

As I got, using must conveys a logical necessity and should means a moral/right thing to do. Then, how could I say such a sentence to convey obligation? I mean to say they were obliged or forced to do something? Is it actually applicable for a past sentence?

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    If you want to show 'force', use 'had'. They had to tell the police.
    – Maulik V
    Commented Nov 19, 2015 at 10:06
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    I don't think either of your suggestions fit your requirements. Keep it simple and use "They had to tell the police".
    – JMB
    Commented Nov 19, 2015 at 10:06

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They must have told the police

This means that it looks like that the police was told some time before. "X must have [verb]" means that the situation looks like that X did [verb].

They should have told the police

This means that they did not tell the police yet, but the situation would have been better if they did tell the police. In general, "X should have [verb]" can mean that if X did [verb] at that past situation, whatever happened would turn out better.

They don't necessarily mean past obligation!

For obligations in the past, I would use

They had to tell the police.

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