Spanish term (edited): dejando constancia del turno elaborada debidamente costurada al expediente

I believe "elaborado/costurado" are typos, and should be "elaborada/costurada" because they refer to the "constancia".
"Del turno" requires a little explanation as it's shorthand for the "juzgado de turno" ("court, among those having the same type of jurisdiction, whose turn it is to manage the case on a given day"; cf. "juez en turno", J. Becerra, Dictionary of Mexican Legal Terminology, 2nd Ed., p. 748).

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Note added at 14 hrs (2023-02-15 16:16:22 GMT)
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To Adrian's point about "turno": no, in my experience, the letter rogatory is drafted by a court clerk, (in the case of divorce proceedings they're called the "secretario/a conciliador/a") rather than the party's own attorney.

cf. Circular CJCDMX -19/2020:
"15.- TRÁMITE DE EXHORTOS, CARTAS ROGATORIAS O REQUISITORIAS.
En relación a las Unidades de Gestión Judicial, los exhortos, cartas rogatorias o requisitorias, serán turnados a quien corresponda, con independencia de que se encuentren laborando a puerta abierta o cerrada.
Respecto a las Salas y los demás Juzgados, solo se les turnarán cuando se encuentren laborando a puerta abierta."
https://www.poderjudicialcdmx.gob.mx/wp-content/uploads/CIRC...