Various volumes and editions online:Hathi Trust: Revised and considerably enlarged edition, prepared by a new and unnamed editor, of Choix des lettres, etc., ed. by J. B. Montmignon, 8 v., Paris, Maradan, 1808-09. V.6. p. 1-331 contains a new introductory account of the discovery of America and of Canada, and letters from missions, as in the Lyons 1819 ed.
Also at BSB, and various other sites.

De rebus Iaponicis, Indicis, et Peruanis epistolae recentiores / a Ioanne Hayo in librum unum coaceruatae.
Reprint. Originally published: Antverpiae : ex officina Martini Nutij, 1605.
Includes index.

The 1605 edition is posted online at the Hathi Trust 

Lettres édifiantes et curieuses de Chine : 1702-1776 / par des missionnaires jésuites ; chronologie, introd., notices et notes par Isabelle et Jean-Louis Vissière.
Bibliography: p. [43]-46.

Der Neue Welt-Bott was a Jesuit missionary periodical written in German and based on the Lettres édifiantes et curieuses. Beginning with translations of French letters, it later became the first serialized publication of German language Jesuit reports from missions worldwide, although today it is best known for its China-related content. Published between 1726-1758 (1761 if missing numbers are included) in 4,500 pages including images, maps, cultural commentary.

For a full description with detailed index of contents, authors, and correspondence, see: Claudia von Collani, "Der Neue Welt-Bott: a preliminary survey" in Sino-Western Cultural Relations Journal XXV (2003) pp. 16-43.

For links to individual numbers see the aggregate page on Bibliotheca Sinica 2.0.

Digital editions also available at HathiTrust and at Heinrich Heine Universität Düsseldorf.

The first volume (8 parts) of the German Jesuit relations, 1642-1726, chiefly from Asia & America, based in part on the French Lettres Edifiantes, in part on the original manuscript reports of the German & other Missionaries; one of the important pieces of German Americana, including, e.g., a map of California & New Mexico; large old bookplate of Joh. Ernst Graf von Kueffstein, engraved by Nicolai, Vienna.--OCLC record.