If you want you can sign up in Inaturalist. In this website you can search the common and the scientific names of this species of Cyanobacteria and other forms of life.

https://www.inaturalist.org/

You can also try http://www-cyanosite.bio.purdue.edu

Alternatively we can help you extract DNA, amplify and sequence the 16S DNA.

Yoram

First of all, that's a nice description about the unknown'. Of course, most of the Myxophyceans are quite difficult to identify. 

& did you check Lyngbya sp? 

& I would suggest http://www.cyanodb.cz/        also... 

All the Best

Anila Ajayan

Dear colleague!

I would like to confirm your suggestion, that your fillamentous cyanobacterium belongs to a species from the class: Oscillatoriaceae. Your species forms long, unbranching filaments inside a rigid mucilagenous sheath. It belongs to the genus Lyngbya.

Please check the link bellow

Best regards

Bohuslav

http://www.cyanodb.cz/Lyngbya

Nice pictures! The first three suggest Lyngbya, but the last one looks different.

Hi people

I want to thank you all for your replies. Frankly, at the beginning I thought that it might be a species of the Lyngbya genus and we have several species her that I identified previously from the intertidal zone, but as Maria Van Herk noted, Fig. 4 (the last one) indicates that it might be something else...

I do own Jiří Komárek big fat book of the Heterocytous genera and species but not the other books of the Oscillatoriales and the Chroococcales. I hope that you have the book regarding the Oscillatoriales....

Yoram, I replayed to you personally