These games do not save the wonder card in their saves, however some details are left behind, in the form of the Wonder Card Records Album (or Gift Records Album).
Findings may be incomplete, until more events gets released.
Starts at 0x45600, taking up every 0x140
|0x45600 to 0x45604||0x000 to 0x004||Epoch Time code of Event received|
|0x45608 to 0x45609||0x008 to 0x009||Wonder Card ID|
|0x4560A||0x00A||Gift Title/Wonder Card Type (as listed below)|
0x01 are for Pokémon type
and 0x02 are for Item type.
|0x4560D||0x00D||Number of kinds of Items, max 06 (for Item-Type gift only)|
|0x4570C to 0x4570D||0x10C to 0x10D||
Species Value for Pokémon
Item ID 1 for Items only
|0x4570E to 0x4570F||0x10E to 0x10F||Amount of Item ID 1, for Item-Type gift only|
|0x45710 to 0x45724||0x110 to 0x124||
Item IDs and Amounts
(2 byte of Item ID, 2 byte for amount, repeat)
|0x45710 to 0x45711||0x110 to 0x111||Move 1 ID, for Pokémon-Type Gift.|
|0x45714 to 0x45715||0x114 to 0x115||Move 2 ID, for Pokémon-Type Gift.|
|0x45718 to 0x45719||0x118 to 0x119||Move 3 ID, for Pokémon-Type Gift.|
|0x4571C to 0x4571D||0x11C to 0x11D||Move 4 ID, for Pokémon-Type Gift.|
|0x45720 to 0x45739||0x120 to 0x139||
Original Trainer (used for Pokémon-Type Gift)
(follows trainer name if it's unset)
|0x4573A||0x13A||Language tag assigned upon being received.|
Gift Title/Wonder Card Type
|ID||Titles ripped from Game Text||Example (based on modifying Counterattack Mewtwo)|
|0||[VAR PKNAME(0000)] Gift||Mewtwo Gift|
|1||[VAR ITEM2(0008)] Gift||
Chesto Berry Gift (modified to item-type)
|2||Item Set Gift|
|3||[VAR 0104(0001)] [VAR PKNAME(0000)] Gift||Genetic Pokémon Mewtwo Gift|
|4||Mythical Pokémon [VAR PKNAME(0000)] Gift||Mythical Pokémon Mewtwo Gift|
|5||[VAR TRNAME(0003)]’s [VAR PKNAME(0000)] Gift||はかせ's Mewtwo Gift|
|6||Shiny [VAR PKNAME(0000)] Gift||Shiny Mewtwo Gift|
|7||[VAR PKNAME(0000)] ([VAR 01CA(0002)]) Gift||
Mewtwo () Gift
* (12) Gift (modified to item-type)
|8||[VAR 01CA(0002)] Gift||
12 Gift (modified to item-type)
|9||Hidden Ability [VAR PKNAME(0000)] Gift||Hidden Ability Mewtwo Gift|
|10||[VAR MOVE(0004)] [VAR PKNAME(0000)] Gift||Psychic Mewtwo Gift|
|11||[VAR PKNAME(0000)] with [VAR MOVE(0005)] Gift||Mewtwo with Shadow Ball Gift|
|12||[VAR PKNAME(0000)] with [VAR MOVE(0006)] Gift||Mewtwo with Barrier Gift|
|13||[VAR PKNAME(0000)] with [VAR MOVE(0007)] Gift||Mewtwo with Calm Mind Gift|
|14||[VAR PKNAME(0000)] & [VAR ITEM2(0009)] Gift||
Mewtwo & None Gift
* & None Gift (modified to item-type)
|15||Downloadable Version Bonus|
|16||Special Pack Purchase Bonus|
|17||Store Purchase Bonus|
|18||Strategy Guide Purchase Bonus|
|21||Virtual Console Bonus|
|22||Pokémon Trainer Club Gift|
|23||Pokémon Global Link Gift|
|24||Pokémon Bank Gift|
Note: The * appears to be based on total amount of records in the album. I've seen the number change when I add or remove records. If you have 6 records, it'll be 6 & None Gift
Can't get WC type 14 to function properly. Keep getting "Mew & None Gift" (Mew intended, None unintended). When I swap past an item entry, the None get's updated to the third item.
Maybe this type is a remnant of Gen 8's system?
WC type 10 seems to work as per normal,
however can't get WC type 11 to 13 to function, even after various tests., and so are the other 3!
I have concluded that it is possibly leftover/unused, as those 3 entries were phrased different from WC type 10, on top of the "not working" issue. Either that, or there's a byte that controls the amount of moves a Pokemon has, and I'm clearly missing it.
Big thanks to @wo0ts for the various contributions for gift records!