The claim sounds about right, giving Alexander's close working relationship with the Golden Horde, but it'd be nice to have a proper confirmation for it.
Alexander Nevsky's helmet hasn't yet been found.
There are two helmets often (mis-)attributed to Nevsky:
- The Helmet of Yaroslav II (Vsevolodovich), shown in Sergei Eisenstein's epic drama „Alexander Nevsky“
- The Helmet of Michael (Fedorovich)
The first thing is that the real helmet of Alexander Nevsky has never been found. However, there are two artifacts often attributed to Alexander.
The helmet of Yaroslav II
It has been found in 1808. Tsarist historians, including A.N.Olenin, the President of Academy of Arts, concluded that the helmet belonged to Alexander Nevsky's father, Yaroslav II. The front plate has an inscription that says:
«Вьликъи архистратиже ги Михаиле помози рабу своему Феодору»
„Great warlord Michael, help your slave Feodor“.
Nevsky's father, Yaroslav, had Christian name Feodor (Theodor). Hence, Olenin suggested that the helmet may have belonged to Yaroslav and then inherited by his son, Alexander.
Considering the location where the helmet was found, Olenin has suggested that the helmet may have been lost during the Battle of Lipitsa in April 1216.
The helmet became extremely popular after Sergei Eisenstein's epic drama „Alexander Nevsky“ (1938).
Actor Nikolai Cherkasov as Alexander Nevsky, 1938.
The Helmet of Michael (Fedorovich)
Jericho Cap of Tsar Mikhail Fedorovich (Russian: «Ерихонская шапка царя Михаила Федоровича») is yet another artifact attributed to Nevsky.
The helmet was crafted in 1621 by Nikita Davydov (Rus.) for Michael I, the king of Moscovia.
It was used as a parade attribute to Michael's dress.
After Moscovia has been renamed to Russian Empire, the helmet was depicted on coat of arms of the Russian Empire.
Nowadays, the helmet is stored in Kremlin Armoury and treated as one of its most valued artifacts.
It has an inscription which can be seen on the top ring of the helmet. It is a quotation from Qur'an 61:13. The text reads:
نَصْرٌ مِنَ اللَّهِ وَفَتْحٌ قَرِيبٌ وَبَشِّرِ الْمُؤْمِنِينَ
And yet another (blessing) that you love: help from Allah and a victory near at hand; and give good news to the believers.
Assuming its well-defined origin, at the time of creation nobody claimed it belonged to Nevsky.
Then, in 19th century, massive rumors emerged claiming that Michael's helmet is not an original one, but a re-mastered helmet of Alexander Nevsky.
There are controversial opinions why such rumors appeared. One point is that Michael, the first tsar of Romanov dynasty, badly needed some proof of inheritance from Rurik dynasty of Kyiv kings.
P.S. It worth to mention that Arabic scriptures on the armory of Moscovian, and then Russian, kings were not a rare thing at all. For instance:
Helmet of Ivan IV The Terrible. Above the Cyrillic text, it also has an Arabic inscription that reads „Allah Muhammad“, according to a Russian official newspaper.
Helmet of tsar Alexis.
Anyway, none of these artifacts are confirmed to belong to Alexander Nevsky.
"Alexander Nevsky helmet" most likely has nothing to do with Alexander Nevski. (Like the "Monomakh Hat"). These are just traditional names, and the objects come from the inventory of the later Russian tsars. They collected beautiful things, and sometimes the most beautiful things were made in the Middle East.
This is the first time I heard this, though I'm generally interested in Russian history, so I am not claiming any authority in my answer.
I posted this query in Russian into Google
шлем александра невского надпись and it returned a list where I have not found any serious mention of this matter. No historical papers, no textbooks, only some blogs, political sites etc.
I searched for all occurrences of the word "helmet" in volume 1 of the Cambridge history of Russia, and have found no mentions of this helmet, though there were no mentions of any Alexander Nevsky's helmet (the search has found about a dozen of occurrences, so I am pretty sure, that I did not miss any).
So I think that this is sort of political propaganda.
That leaf-shaped device on the helmet of Tsar Alexis actually contains the complete Muslim profession of faith (shahâda), “There is no god but God, Muḥammad is the messenger of God” (Lâ ilah ilâ Allâh, Muḥammad rasûl Allâh). It’s quite legible, starting at bottom right and reading left, then up, roughly:
الله — Allâh
رسول — rasûl
محمد — Muḥammad
لا اله الا الله — Lâ ilah ilâ Allâh