שְְׂרָָף... לִִשְְׁלִִישׁוְְלִִרְְבִִיעַַ or שְְׁרָָף... לְְשָָׁלִִישׁוּלְְרָָבִִיעַַ

As far as I am aware, s'faraddim and b'nei 'edah mizraħit (with the exception of teimanim) have שְְׁרָָף... לְְשָָׁלִִישׁוּלְְרָָבִִיעַַ

However, the teimanim who follow nosaħ shaami (the s'faraddi-style import) nevertheless have שְְׂרָָף... לִִשְְׁלִִישׁוְְלִִרְְבִִיעַַ

i. why is שרף being spelled here with שׁ instead of שׂ; and

ii. what has שָׁלִישׁ, the helper of a king, to do with קטורת?