Ithaca 1911a1 barrel question

Hello was able to buy what I think is an original Ithaca 1911a1,finish looks to be 90%,all markings are present.
The barrel has a P on the left side bottom and a F on the r side which I think the F stands for flannery bolt company.
Could the flannery barrel be original for this gun,the barrel is blued with matching wear.
the pistol was in a black buchenheimer holster with the original pistol belt wraped around it.will post pics when I figure out how.

thanks

although th e majority of Ithaca were HS barrels quite a few came with flannery barrels.