There is no mobile Windows versions of Firefox as Mozilla only supports Android and iOS.

Mozilla has no plans to support Windows Phones OS's and less likely with its ever decreasing low market share. If Mozilla had been supporting Windows Phones they likely would have discontinued sometime ago.

As I indicated, I know that Mozilla does not have an app for my problem. That is why I still have the question of there is another solution to use "Firefox Sync " on my windows mobile.

HI, Sorry no there is not.

JanhH said

As I indicated, I know that Mozilla does not have an app for my problem. That is why I still have the question of there is another solution to use "Firefox Sync " on my windows mobile.

Since Firefox sync is for between different devices with Firefox and not different web browsers then no.