A step beyond storing organic material...storing DNA digitally.
In about 60-80 years, according to Kepler's law and ceteris paribus, the normal-sized hard drive will be 1 yottabye. The cost to produce that today would be about $100 trillion.
That to say, technological advances should make it possible to store the extensive, but tiny bits of "code" in DNA, as a common thing.
One doesn't need to speculate too hard to think it could be possible to reverse the concept...instead of just "reading" the DNA data to a hard drive, one could also "write" out the sequence, which could be implanted into a cell. And presto! Immortality...of a sort.