The official Japanese Movie 22 website has updated with information on the annual movie drawing contest. Translations follow:

Organized by 12 Shogakukan magazines! The Mewtwo Strikes Back Evolution Drawing Contest

We are holding a mass commission for your Pokémon drawings!
Color in the specified submission forms, draw whatever Pokémon and pictures your want around them, and complete the drawing according to the provided theme!
Believe it or not, the drawings selected as the grand prize winners will appear in this year's movie alongside the names of the winners!

Draw wonderful drawings and send them in en masse!

Themes


For Pokémon Fan, Kindergartener Magazine, Shogakukan Kids, TV-kun, Corocoro Comic, Corocoro Ichiban!, Shonen Sunday and Corocoro Aniki: Draw a cool battle scene featuring "Mewtwo", the Pokémon that appears in this year's movie!
For First Grader Magazine, Pucchigumi and Cíao: Draw a scene featuring "Mew", the Pokémon that appears in this year's movie, happily playing!
For Sunday Web Every X Pixiv: Draw freeform, using "Mewtwo" and "Mew" as your themes!

The Grand Prize (1 winner from each magazine, for a total of 12 winners)


*The Nintendo Switch game "Pocket Monsters Let's Go! Pikachu / Let's Go! Eievui" (pick one) + one "Monster Ball Plus"
Prize provided by: Pokémon
*Your drawing and your name will be presented in the movie

The Runner-Up Prize (5 winners from each magazine, for a total of 60 winners)


*A set of MonCollé EX "Mewtwo" and "Mew" figures
This is a set of Mewtwo and Mew, who both play a role in the movie!
Prize provided by: Takara Tomy


Submission rules (read through these with an adult):
If sending in the specified submission forms included with the various magazines:
Cut out the submission form from one of these magazines, finish your drawing, fill in your address, name, phone number, gender, grade and name of other person in the household, then send it in.
If sending in a downloaded submission forms:
Download one of the submission forms from below, print it out, cut it out following the dotted lines, finish your drawing, fill in your address, name, phone number, gender, grade and name of other person in the household, then paste in on the front (the part you write the address on) of a postcard or standardized postcard. Paste your drawing on the back of the postcard, then send it in.
If you're not using a standardized postcard, don't forget to add a 62 yen stamp.

Pokémon Fan, on sale February 28th
Kindergartener April issue, on sale February 28th
TV-kun April issue, on sale February 28th
First Grader April issue, on sale February 28th
Pucchigumi April issue, on sale March 1st
Ciao April issue, on sale March 3rd
Corocoro Comic April issue, on sale March 15th
Corocoro Aniki Spring 2018 issue, on sale March 15th
Shonen Sunday, on sale March 20th
Corocoro Ichiban May issue, on sale March 20th
Shogakukan Child Education Division Web Site Shogakukan Kids, starts taking submissions March 4th
Sunday Web Every X Pixiv, starts taking submissions March 15th
"Sunday Web Every" allows you to submit freeform drawings online, no paper needed!

*All rights relating to the winning drawings (including the rights provided in Article 27 and Article 28 of the Copyright Law) shall belong to The Pokémon Company. 
Winners will not exercise any moral rights to winning drawings.
*Please note that submitted drawings can not be returned.
*Please go here for information on the handling of personal information sent with the drawings.


Announcement of winners:
Winners of the grand prizes will be announced in the movie itself alongside the winnners' names and drawings. All winners will be announced in each magazine and on the official movie website.

Jury:
Tsunekazu Ishihara, Kunihiko Yuyama, Ken Sugimori, Masakazu Kubo, Junya Okamoto, Hidenaga Katakami, Toho's advertising managers, each magazine's editor-in-chiefs (listed in no particular order)

Source: http://www.pokemon-movie.jp/illust_contest/