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Recently, I played a warlock in a 5e one-shot. We were playing at level 7 and I was a Pact of the Blade warlock with the Fiend patron. As a Fiend Warlock, I have a feature called "Dark One's Blessing", :

Starting at 1st level, when you reduce a hostile creature to 0 hit points, you gain temporary hit points equal to your Charisma modifier + your warlock level (minimum of 1).

The description of the Armor of Agathys spell reads:

A protective magical force surrounds you, manifesting as a spectral frost that covers you and your gear. You gain 5 temporary hit points for the duration. If a creature hits you with a melee attack while you have these hit points, the creature takes 5 cold damage.

At Higher Levels. When you cast this spell using a spell slot o f 2nd level or higher, both the temporary hit points and the cold damage increase by 5 for each slot level above 1st.

The situation was that there was a pack of 'minions' (4th-edition term, I know... but they were low-AC 5 hp monsters that died in 1 hit most of the time) attacking my group. The dragonborn wizard knew Fly, and grabbed the halfling and flew out of reach of the group of minions; I was left there with Armor of Agathys cast on me at level 4, so I had 20 temp hp and did 20 damage to each minion.

The question comes from the functionality of Temp HP (THP)... It does not stack. Instead, you must choose which set to acquire, either keeping the THP you currently have or using the new number provided by whatever is trying to give you more THP.

Once I was below 20 THP from the attacks made on me by this swarm of minions, I started taking the 10 (warlock level + CHA mod= 7+3) THP provided by Dark One's Blessing. After rereading Armor of Agathys today, I noted it says 'while you have these hit points'... leading me to believe that choosing to take the 10THP from Dark One's Blessing would remove the Armor of Agathys and its damaging capability.

TL;DR

Does Armor of Agathys only work if you have THP from the spell specifically, or does it still work if you gain more THP from another source (like from Dark One's Blessing) while the spell is still active?

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It seems like you have come to the conclusion yourself, just unsure which to apply.

The rules seem clear, as you described from PHB pg 198

"...they (temporary hit points) can't be added together. If you have temporary hit points and receive more of them, you decide whether to keep the ones you have or gain new ones..."

Armor of Agathys: You gain 5 temporary hit points for the duration. If a creature hits you with a melee attack while you have these hit points ..."

These being from the Armor of Agathys spell specifically.

Dark One's Blessing: "...you gain temporary hit points equal to..."

So the moment you reduce a creature to 0 hp it says you automatically gain temporary HP as part of Dark One's Blessing. If you choose to take these hit points, then Dark One's Blessing overwrites your Armor of Agathys. Imagine it in context. You cast Armor of Agathys, the temporary hp takes the form of a spectral frost that covers your body.

The moment you kill something and your patron, 'The Dark One' , reaps their life energy and you choose to take a portion of it, that spectral frost disappears in place of a stronger buffer of dark essence swirling around you from the monster you just killed. No more Armor of Agathys, and thus the spell ends and it's effect no longer applies.

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You must have the temporary hp from armor of Agathys active. You can only have one source of temporary hp at any given time.

PHB p. 198 (or here in the Basic Rules) states:

Healing can’t restore temporary hit points, and they can’t be added together. If you have temporary hit points and receive more of them, you decide whether to keep the ones you have or to gain the new ones. For example, if a spell grants you 12 temporary hit points when you already have 10, you can have 12 or 10, not 22.

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