Eating Before Tashlumin Prayer

I woke up after midnight and need to pray Mincha twice. Is it permissible to eat before the Tashlumin Shacharit prayer?

Before you have prayed Mincha, it is forbidden to eat (though the elderly and weak are permitted, and it is also permitted to drink coffee), similar to the rule for eating before Shacharit. Even after praying Mincha, before the Tashlumin Shacharit prayer, one should not eat because it is necessary to connect the Tashlumin Shacharit prayer to the Mincha prayer as closely as possible. If one ate between the two prayers, they can pray the Tashlumin prayer and stipulate that if they cannot complete it due to the interruption, it will be considered a voluntary prayer.

In the Gemara in Berachot, page 10, it is explained that one should not eat before the Shacharit prayer. This rule is connected to the verse "do not eat on the blood," meaning "do not eat before you pray for your blood." It is written: "and you have cast Me behind your back," do not read "your back" but "your pride." After one has become proud through eating, he accepts upon himself the yoke of the kingdom of heaven. Therefore, if he has not prayed Shacharit and needs to make it up in the Mincha prayer, he is forbidden to eat before this because he has not yet accepted upon himself the yoke of the kingdom of heaven. The early commentators derived from the words of the Gemara that it is specifically with pride that it is forbidden, but drinking water is permitted, and it is also permitted for the elderly or sick. Regarding the prohibition of eating between the Mincha prayer and the Tashlumin prayer, it is because it is necessary to connect the Tashlumin prayer to the Mincha prayer. This is explained in "Machatzit HaShekel," Orach Chaim, Siman 108, Se'if Katan 3, where it says: "However, it is written in Se'if 3 that it is only completed during the time of prayer. And it is written in the book 'Eliyah Rabbah' [here Se'if Katan 4] in the name of 'Perisha' [letter Bet], that one should not delay more than the time it takes to walk four cubits or say 'Ashrei,' and immediately pray the Tashlumin prayer. And if he is engaged in a meal and does not interrupt, there is no doubt that he delays more than this time, and how will he complete it after his meal." However, in "Mishnah Berurah," Siman 108, Se'if Katan 15, it is brought that there are those who say that the rule that one must complete during the time of prayer means within the time when it is permitted to pray Mincha and not after sunset. And it concludes that if one interrupts, he should stipulate that if according to those who say it is forbidden to interrupt between prayers, his prayer will be a voluntary one.