Question

he said to his friend,"let us go out" change narration​

Answer 1

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He proposed to his friend that they should go out.

Explanation ↴

Like Imperative sentences, use of 'Let' in the sentences of Let has different meaning and in Reporting Verb 'Said To' is replaced according to the notion of the sentence with words like - Proposed, Suggested, Requested, Ordered, Wished, Told, etc.

↬ If the meaning of 'Let Sentence' is a suggestion, proposal or wish then for making Indirect Speech (1) 'Said To' is replaced with 'Proposed To / Suggested To / Wished To', (2) 'Let' is replaced with 'Should'. 'Should' comes after the Pronoun. and (3) 'That' is used to join both the parts of the sentence.

↬ If the meaning of 'Let Sentence' is to allow, order or persuade then for making Indirect Speech (1) 'Said To' is replaced with 'Requested To / Ordered To', (2) 'Let' may remain in the sentence or it may be replaced with 'Allow' and (3) 'To' is used to join both the parts of the sentence.

↬ If condition or supposition comes in 'Let Sentence' then for making Indirect Speech (1) 'Said To' is replaced with 'Told', (2) 'Let' is replaced with 'Might' and (3) 'That' is used to join both the parts of the sentence.