You don’t even have to do that. Just get the immortal person in question to cut his hand and get the other person to drink it.
Depending on the scale and power of the Immortality:
Eternal Youth: not really do much besides a health potion like effect.
Got this idea from the Vampire Diaries
Deadpool/Ban Level: completely heal the person of all physically damage, boost back to full strength and depending on how much they drink, give a physical enhancement.
Absolute: literally give the drinker Immortality. Because the blood is apart of a Absolute being. It gives the drinker Immortality even if it’s one drip he drank. This is because blood that is eternal is now In them. Making them eternal as well. They could possibly have it taken out though through blood extraction or manipulation.