Book of Going Forth by Night vs. Shambling Hordes

According to Shambling Hordes text, it cannot gain life. According to Book of Going Forth by Night, the stolen ally gains a life if it has no life. Does that mean that a Shambling Hordes that's burned and stolen by someone with Book of Going Forth by Night will immediately burn again?

Shambling Hordes
Necromancy
Zombie with 3 life. 0 strength, 0 bleed.
nec After this ally enters play, remove an ally or vampire in your ash heap from the game or burn this ally. This ally gets +1 strength for each life it has. This ally can enter combat with a minion as a Ⓓ action. It cannot gain life (instead, any life it would gain goes to the blood bank).
NEC As above, but this ally has 4 life.


Book of Going Forth by Night, The
Unique.
This vampire gets superior Serpentis SER. If an ally opposing this vampire in combat would be burned, instead steal and lock the ally; if the ally has lost their last life, they gain 1 life.

I'd say yes - assuming SH has no life.

KoRnesshon is correct, Shambling Horde would still burn if stolen without life as it cannot gain life.. similar to that Heaven’s Gate doesn’t prevent Shambling Hordes from burning if it has no life. [LSJ 20051117]