The only direct link that I know between Zoroastrianism and Islam is the adoption of symbols by Islam from Zoroastrianism as well as a few architectural notions. Aside from these adoptions, there has been little to suggest that there was a massive adoption of anything similar. This area of study is hard to perform as both sides of the argument tend to over-inflate what the other did/did not contribute. Currently the group with the largest voice in this debate are exiled Iranians who think almost everything was adopted by Islam which simply isn't true.
Firstly, the symbol of the moon and star that is commonly seen throughout the Islamic world was originally a symbol from Zoroastrianism. However, that symbol was not tilted to the extent that is used currently. There has been no defining research as to why the symbol was adopted and why it became tilted as it has.
Secondly, the adoption of architectural forms found in places like the fire-temples of Zoroastrianism turned into giving Muslims an idea of how to build their mosques. Most are open on 4 sides, as are fire temples and central to the courtyard, before the main prayer area, there are usually fountains or washing stations to preform ablutions. This was taken where the in the centre of the first temple would be the central fire said to have continued from the time of Zoroaster and was considered extremely holy.
I'll provide a few sources, but like I said there is a lack of study in this area that I know of.