The phrase "Please Keep in Touch," is kit full form, meaning ""Please Keep in Touch."" To continue conversing or discussing an issue with the person to whom the letter or written communication is addressed, this term is most typically used in written communications or letters (both personal and business).
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This is a typical type of formal request that is often substituted for Stay in Touch. People use the abbreviation KIT while talking with others.

The abbreviation KIT is used to show sincerity and genuine kindness toward another person.
It indicates that the person who penned these three letters – K-I-T – in the letter or formal communication desires to preserve strong business relations."