Can Fraz-Urb’Luu make use of a Wish spell from his one-minute Simulacrum (‘in-Lair’ action)?

As a demon Lord, Fraz-Urb’Luu has many powers. Specifically he can generate a Simulacrum of anyone in his ‘lair’ – and they last for about ten seconds, give or take. Specially:

Fraz-Urb’luu chooses one humanoid within the lair and instantly creates a simulacrum of that creature (as if created with the simulacrum spell). This simulacrum obeys Fraz-Urb’luu’s commands and is destroyed on the next initiative count 20. – Mordenkainen’s Tome of Foes pg. 146.

How much time does Fraz-Urb’luu have with this simulacrum? Let us assume he has some kind of 17th level caster on hand (possibly Petrified or Imprisoned) – and this humanoid happens to be a caster that has Wish in their memory-repitoire (i.e. a wizard or bard with a Magic Secret). Possible time-flow in bullet-point format:

  • Fraz-Urb’luu must explain to his newly minted simulacrum-creature what it wants it to do. If it wants that illusion-person to cast Wish, this demon lord must explain / include wording of the spell. Not sure how many move-actions this would be. This lord does have telepathy (one of his ‘languages’), which might help.

  • The creature must cast the spell, this is probably one move-action.

  • The creature must include anything it wants with the spell. This would include the full wording of this Wish as indicated by their master Demon Lord creator just moments ago. This may not count as a second move action (?), but it would still require the (re)-wording of the entire phrase once more. Any extensively worded wish will obviously not fit in this time-frame.

How much time do they have together? What RAW exists around the timing, sum total, including this "next initiative count of 20"?

Question: How much time will the Great Demon Lord Fraz-Urb’luu have with his Lair-based Simulacrum from the moment of this casting & creation of his duplication-creature to the end of that creature’s life at the end of the next round?

Reason For Asking: In my campaign world this Demon Lord would like to have the ability to cast Wish (and other spells) in his ‘home’ or lair via this clever mechanic. He also has 26 intelligence and 24 wisdom – he would be intelligent enough to figure out how to do this. This mechanic would be valuable not just for defending himself from brazen adventurers &/or unhappy demon-lords but is also excellent for entertainment &/or creative purposes. Casting a single limitless Wish every second round would be a very useful tool to have.

Edit: Other creatures have a similar mechanic, a DM-option allows this for certain hags:

A powerful sea hag might (?) have the following additional lair actions:

The hag chooses one humanoid within the lair and instantly creates a simulacrum of that creature (as if created with th esimulacrum spell). This hideous simulacrum is formed out of seaweed, slime, half-eaten fish and other garbage, but still generally resembles the creature it is imitating. This simulacrum obeys the hag’s commands and is destroyed on initiate count o20 on the next round. – Volo’s Guide To Monsters, pg. 60.