The counters do not technically move¹, however the identical quantity of counters are placed on one other creature.

When playing cards point out energy with out explicitly mentioning “base energy”, it at all times means the precise energy of the creature, considering all +1/+1 counters, static buffs, and naturally base energy (the identical is true for toughness respectively, after all).

That is additionally indicated in Dying’s Presence‘s oracle textual content:

X is the ability of that creature because it final existed on the battlefield.

¹ The rationale I point out that counters do not technically transfer is that for a 2/2 creature with two +1/+1 counters, you’d nonetheless place 4 counters on the goal creature with Dying’s Presence, not two – phrasing it as “transferring counters” is likely to be complicated on this regard. There are playing cards in magic that really transfer counters, resembling Bioshift, and in case of this instance creature, they might solely put two counters on the goal creature.