The Customs Rules

The Russian Federal Customs Service has a webpage detailing the items that are controlled and/or prohibited for importation in Russia. In relation to weapons it states:

Goods, prohibited or limited for transfer via the customs border of the Eurasian Economic Union

(in accordance with the decision of Board of the Eurasian Economic Commission dated April 21, 2015 No 30 “On non-tariff regulation measures”)

List of the goods for the personal usage, prohibited to import into the customs territory of the Eurasian Economic Union (hereinafter - the Union) and (or) export from the territory of the Union

1 - In case of transfer via the customs border by any means:

[...]

1.2 - service and civilian weapon, its major parts, and ammunition to it, prohibited for import and(or) export (section 1.6 of the Decision)

and

List of the goods for personal usage, limited to import to the territory of the Union and(or) export from this territory

4 - In case of transfer via the customs border by any means:

[...]

4.3 - Service and civilian weapon, its major (constituent) parts, and ammunition to it (section 2.22 of the Decision, Attachment No 17)

The Decision detailing which weapons are prohibited and which are limited for importation can be found here. The relevant sections are: section 1.6 and section 2.22. Both these documents are in Russian but they can easily be parsed via Google Translate.

What Are Major Contituent Parts of Firearms?

Doing so reveals that section 1.6 relates mostly to automatic weapons, gas weapons, radioactive ammunition, explosive cartriges, butterfly knives, and all such items whose importation one would expect to be prohibited by common sense. Section 2.22 instead relates to sport and hunting weapons, both cold weapons and firearms. In section 2.22 one can find an explanation of what is meant by "its major (constituent) parts". These seem to mean:

14. The main (component) parts of pistols and sporting revolvers

15. The main (component) parts of pistols and service revolvers

16. Trunks of hunting and sport smooth-bore rifles and carbines

17. Trunks rifled hunting and sports rifles and carbines

18. Other main (component) parts of hunting and sport smooth-bore guns (bolt, drum, frame, receiver (block), forend, trigger mechanism and parts and accessories to it)

19. The main (component) parts of sports rifles , hunting carbines, rifles with a rifled barrel (barrel, bolt, drum, frame, receiver (block), forend, trigger mechanism and parts and accessories to it)

This list does not include stock, sling and grip. This means that, in principle, you should be allowed to import these three items into Russia. However, to be extra safe and since I am not a lawyer, you should probably go ahead and declare them at customs and have the officers check this for you.