Which after blessing is to be recited first; Borei Nefashos or Meiyn Shalosh?

The after blessing of Meiyn Shalosh is of greater status than the after blessing of Borei Nefashos. Accordingly, the Poskim[1] rule that one is to be precede the blessing of Meiyn Shalosh to the blessing of Borei Nefashos. Thus, if one ate a food of the seven Minim and a food that requires Borei Nefashos, he is to first recite Meiyn Shalosh and only afterwards recite Borei Nefashos.

The law if the first blessing over the Borei Nefashos food was preceded due to being more Chaviv: Some Poskim[2] rule that in the event that the Borei Nefashos food was more Chaviv/beloved, and according to Halacha had its first blessing precede the first blessing of the Meiyn Shalosh food [such as by a Haeitz/Hadama mixture], then so too, its after blessing of Borei Nefashos is to be preceded to Meiyn Shalosh. Thus, if one had raisins and strawberries in front of him, and he preceded the strawberries in the blessing of Hadama, due to it being more beloved, then so too he is to precede its blessing of Borei Nefashos.

The order of after blessings:

1. Birchas Hamazon
2. Meiyn Shalosh
3. Borei Nefashos

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[1] P”M Pesicha 202:10; Ashel Avraham Butchach end of 211 “All the Dinei Kadimos apply likewise by the after blessing. This law is clear and solid without any doubt or question. It is a great wonder that it was omitted from the Achronim”; See Admur 202:12; Seder 7:13,  Luach 10:13 the order “so he can bless Meiyn Gimel and Borei Nefashos”; Piskeiy Teshuvos 212:10

[2] Ashel Avraham ibid at first questions this idea and the concludes that based on logic Chaviv applies even by a Bracha Achrona; Piskeiy Teshuvos ibid