For reference, Hauke's edit refers to a new Matplus.net Forum thread. Here are diagrams for each game.
Challenge A: White Stalemates Black
[Title "Arno Tungler, Matplus.net Forum 11/22/2021, ser-=19"]
[FEN ""]
1. d4 null 2. d5 null 3. d6 null 4. dxc7 null 5. cxb8=R null 6. Rxc8 null 7. Rxa8 null 8. Rxa7 null 9. Rxb7 null 10. Rxd7 null 11. Bg5 null 12. Bxe7 null 13. Bxd8 null 14. Rxf7 null 15. Rxg7 null 16. Rxh7 null 17. Rxh8 null 18. Rxg8 null 19. Qd5=
Challenge B: White Stalemates Themselves
Original Source: https://www.france-echecs.com/article.php?art=20010824124929501
[Title "Michel Caillaud, France Echecs 4/5/2004, ser-=51"]
[FEN ""]
1.a4 null 2. a5 null 3. a6 null 4. Ra3 null 5. Rf3 null 6. Rxf7 null 7. Nc3 null 8. Nd5 null 9. Nxe7 null 10. Nxg8 null 11. b4 null 12. b5 null 13. b6 null 14. bxc7 null 15. cxb8=R null 16. Ba3 null 17. Bxf8 null 18. c4 null 19. c5 null 20. c6 null 21. cxb7 null 22. bxc8=N null 23. Nce7 null 24. Rb6 null 25. Re6 null 26. d4 null 27. d5 null 28. d6 null 29. Qd2 null 30. Qh6 null 31. e4 null 32. e5 null 33. h4 null 34. h5 null 35. Rh3 null 36. Rg3 null 37. Rgxg7 null 38. Kd2 null 39. Kd3 null 40. Ke4 null 41. Kf5 null 42. Kf6 null 43. Bd3 null 44. Bg6 null 45. f4 null 46. f5 null 47. Nh3 null 48. Ng5 null 49. Nxh7 null 50. g4 null 51. g5!=