As @LauraDoherty said,
\Have a look at this discussion, it explains it.
Basically, "le = with" whilst "le + an -> leis an = with the".
That's just the way it is: the "-n" of "an" is dropped in running speech (except before a vowel). I remember it being one of the first things a "mother-tongue" speaker of Irish pointed out to me when I was learning Irish the first time around. (That was nearly 50 years ago, so I've had plenty of time to forget nearly all of it; which is why I'm beginning again now with duolingo!)
i think her pronunciation of oibríonn is just a dialect difference... other dialects pronounce is more like ih-breen, or ih-breeun. you can hear the regional differences here: https://www.teanglann.ie/ga/fuaim/oibrigh
that said, i think the very slenderly-pronounced l is what has you hearing a v sound. i can hear the 'l' when i listen carefully, but it does almost disappear into more of a 'y' as mentioned above by murakel.
i also didn't hear the 'n' in 'an'... which i think is pretty common in normal spoken irish, that sometimes those little particles get shortened or dropped (for example, 'agus' shortening to 'is' or 's' in speech and even writing). but it sure did make it difficult to understand what i was supposed to be typing.
so if she had pronounced this a bit more slowly and clearly, and if you wrote it out following the word breaks rather than the way it naturally flows together in her speech, phonetically it'd look something like: eye-breen shee lyesh uhn vhahr.
Even if there was a mysterious V sound (there isn't), the vowel sound is clearly not the sound of the i in sibh.
You can slow the audio down by open it directly in your browser, and right-clicking on the player control in the browser window to set the Play Speed to 0.5
(This works best in Microsoft Edge - Firefox just chops up slowed down audio. You can also open the URL in VLC or other players that allow you to open network streams).
Most of the time, a preposition+an will cause either séimhiú or urú on the first consonant of a following noun. (Preposition+an always causes séimhiú in Ulster Irish.) You can look up the prepositions here: (nualeargais.ie/gnag/praepos.htm) to see what each does.
In the example you are asking about, both 'leis an bhfear' (v-sound) and 'leis an fhear' (fh is silent, but you would pronounce the n of 'an') are correct, depending on your dialect.
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