In which country was a cordless telephone developed within nineteen months (in 1979) that was suitable for establishing a wireless voice telephony network to serve remote villages in the Mexican state of Guerrero?

The first mobile phone network was developed in the former East Germany.

Blaumeise 3 was the internal designation for the first mobile phone in East Germany .It was developed in 1979 at VEB Funkwerk Köpenick in Berlin, a subsidiary of VEB Kombinat Nachrichtenelektronik . The reason for its development was a contract to build a radio network for voice telephony in Mexico to serve remote villages in the Mexican state of Guerrero . It consisted of permanently installed telephones connected to the existing landline network via a radio network. The device transmitted on the URTES network (UHF radio-telephony system) and was equipped with a conventional pulse dial . Its formal designation was UDS 721 U. It weighed 10 kg and had a range of over 40 km. The Stasi assigned it the internal code name Blaumeise 3 (Blue Tit 3 ).

https://de.wikipedia.org/wiki/Blaumeise_3
https://www.volksstimme.de/sachsen-anhalt/regionale-wirtschaft/handys-aus-der-ddr-kamen-in-mexiko-gross-raus-454944

This is a very specific question. Some more context.

The commission came in 1979, but was not completed until 1981, as is implied in the question.
"Am 12. September 1981 nahm DDR-Staatschef Erich Honecker in Mexiko das Netz in Betrieb."

There are other milestones

First Wireless Conversation (1880): Alexander Graham Bell and Charles Sumner Tainter invented the Photophone, which successfully transmitted a voice message wirelessly over a beam of light, rather than radio waves.

https://www.optica-opn.org/home/articles/volume_4/issue_6/features/alexander_graham_bell_s_photophone/

First Practical Wireless Telephone (1912): Japanese inventor Dr. Torigata Uichi created the "T.Y.K. wireless telephone system." It was the world's first practical, long-range wireless voice communication system that predated vacuum tubes. (Super cool looking, check it out!!)

https://www.postalmuseum.jp/column/collection/tykwirelesstelephone.html

First Commercial Cellular Network (1979): The first full-scale, commercial cellular network was launched by Nippon Telegraph and Telephone (NTT) in Tokyo, Japan.

https://en.wikipedia.org/wiki/1G


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It was developed within nineteen months; the installation in Mexico took until 1981!