Fonts & Character Sets ⇒ Cyrillic "і" encoded as latin "i"

[IhorB]

Hello!
I've just started using LaTeX so sorry if this was asked before. Unfortunately I wasn't able to find any answers.
I created few documents in Ukrainian language using packages babel with option Ukrainian, inputenc with cp1251 (as I use OS WINDOWS), and fontenc with encoding T2A which as far as I understand is standard for Ukrainian. Also I use package cmap to produce searchable pdf-files. So in preambula I have:

\usepackage{cmap}
\usepackage[T2A]{fontenc}
\usepackage[cp1251]{inputenc}
\usepackage[ukrainian]{babel}

It all works fine except one small detail. It looks as cyrillic letter “і” is encoded as latin “i”. Of course it doesn’t create too much problem as they look the same, but searching pdf or copying from it may be problematic. Can anyone help me with this?
Thank you in advance for any suggestion!