What's an expression for a cunningly-fake friend?

"Silver-tongued devil" accurately describes many politicians, whose "fluent and persuasive speech" has gotten them where they are (the Free Dictionary), but to fit your scenario, I'd use it with one (all?) of your suggestions to fully capture the "backstabbing" notion : "a two-faced, backstabbing, snake-in-the-grass, silver-tongued devil."

For a single word, there’s an "opportunist,” who is someone that “seizes every opportunity to improve things for him/[her]self”), including “act[ing] as if they are close friends.” (Vocabulary [dot] Com).

To the extent that not all “opportunists” are wise enough to successfully execute their schemes, you could add a modifier such as “conniving [opportunist]” or “calculating [opportunist]”, to help your friend see what you see in his/her manager.

A simple adjective is

devious

Showing a skillful use of underhanded tactics to achieve goals

but I prefer

Machiavellian

using clever lies and tricks in order to get or achieve something

clever and dishonest suggesting the principles of conduct laid down by Machiavelli; specifically : marked by cunning, duplicity, or bad faith

Not exactly a "real" word, although some dictionaries now list it, but how about "Frenemy"?

one who pretends to be a friend but is actually an enemy

Judas, though that may only be relatable to people familiar enough with the biblical story of Judas Iscariot:

The term Judas has entered many languages as a synonym for betrayer, and Judas has become the archetype of the traitor in Western art and literature. Judas is given some role in virtually all literature telling the Passion story, and appears in a number of modern novels and movies. (Wikipedia)

The story of The Scorpion and the Frog also comes to mind, though the scorpion in that case is betraying because it's in his nature; looking at that page lead me to this quote that perhaps gives a better word than snake, "viper":

It is this moral that is also illustrated by Aesop's fable of The Farmer and the Viper, where a farmer saves a snake which then bites its benefactor as soon as it has recovered. The farmer's last words are, "I am rightly served for pitying a scoundrel" and the moral is "The greatest kindness will not bind the ungrateful." (Wikipedia)

The character Achilles De Flandres in the Ender's Shadow series is much like what you describe. Quoting from the link:

Achilles de Flandres is the main villain of the Bean quartet. Like Bean, he grew up in Rotterdam, an orphan on the streets; like Peter, he displays sociopathic tendencies, particularly by murdering anyone who has ever seen or made him helpless. (Wikipedia)

Emphasis mine. His character is portrayed as being unusually skilled at eliciting love, respect, and trust from others; he then betrays them if it is convenient, without any remorse. I mention this reference more to point out his sociopathic tendencies.

The character Wormtongue from Lord of the Rings also bears some similarities. The character is exceptionally good at gaining positions of trust/authority. The name alone carries with it some connotations even if the recipient isn't familiar with Lord of the Rings.

Worm (and derivatives thereof), when used to describe people, may be used in a number of ways including:

3 [count] informal + disapproving : a person who is not liked or respected : a very bad person

• I didn't think that she would go on a date with that worm. [=wretch]

worm into [phrasal verb]

worm (your way or yourself) into (something) informal

to get (yourself) into (a desired position, situation, etc.) in a gradual and usually clever or dishonest way

• I wormed my way into a job at the theater.
• He somehow managed to worm himself back into her life.

(learnersdictionary.com)

The urban dictionary definition for wormtongue says:

A “ Worm Tongue” is a cunning, lying “sack of shit” Troll who for some reason is able to incredibly manipulate people to evil ends with their voices. The trance that worm tongues put their victims into is similar to a snake that hypnotizes its prey, before it eats them.

Most televangelists, used-car salesmen, politicians, hookers, drug dealers and lawyers have worm tongues and have to the power to seduce people with their voices.

The origin of the worm tongue is most-likely the character created by J.R.R. Tolkien in “The Lord of The Rings” trilogy.

Len is sure one mother-fucking worm tongue. I have never seen one person create so much stink between people in such a long time. (urbandictionary.com)

If we are considering literary references, perhaps Do not trust him! He is a Iago!

Iago is a Machiavellian schemer and manipulator, as he is often referred to as "honest Iago", displaying his skill at deceiving other characters so that not only do they not suspect him, but they count on him as the person most likely to be truthful.

Wikipedia