The M”B in Siman 108 Sif-Katan 4 brings that someone who missed a tefillah and is now the shliac tzibbur may use the chazaras ha’shatz for his tashlumim.
(makor in Radbaz see here: http://www.hebrewbooks.org/pdfpager.aspx?req=1952&st=&pgnum=130 siman 361.)
L’maseh the radbaz says it, but why? The shliach tziibur is a shliach to daven mincha for the tzibbur how can he also have kavana for the tefillah to be good for his teshlumim from shachris?
Answer:
The reason for this is that the tashlumin for Shacharis is to daven Minchah twice. Therefore, the fact that the chazan has intent for his tashlumin does not make his davening into a Shacharis, because on the contrary his tashlumin is to daven Minchah again, which is what the tzibbur also require.
Best wishes.
