  Born-again stars allow probing stellar evolution in human timescales and
provide the most promising path for the formation of hydrogen-deficient
post-asymptotic giant branch objects, but their cold and molecular components
remain poorly explored. Here we present ALMA observations of V605 Aql that
unveil for the first time the spatio-kinematic distribution of the molecular
material associated to a born-again star. Both the continuum and molecular line
emission exhibit a clumpy ring-like structure with a total extent of
$\approx$1$^{\prime\prime}$ in diameter. The bulk of the molecular emission is
interpreted as being produced in a radially-expanding disk-like structure with
an expansion velocity v$_{\rm exp}$$\sim$90 km s$^{-1}$ and an inclination
$i$$\approx$60$^{\circ}$ with respect to the line-of-sight. The observations
also reveal a compact high-velocity component, v$_{\rm exp}$$\sim$280 km
s$^{-1}$, that is aligned perpendicularly to the expanding disk. This component
is interpreted as a bipolar outflow with a kinematical age $\tau$$\lesssim$20
yr, which could either be material that is currently being ejected from V605
Aql, or it is being dragged from the inner parts of the disk by a stellar wind.
The dust mass of the disk is in the range $M_{\rm
dust}$$\sim$0.2-8$\times$10$^{-3}$ M$_{\odot}$, depending on the dust
absorption coefficient. The mass of the CO is $M_{\rm
CO}$$\approx$1.1$\times10^{-5}$ $M_{\odot}$, which is more than three orders of
magnitude larger than the mass of the other detected molecules. We estimate a
$^{12}$C/$^{13}$C ratio of 5.6$\pm$0.6, which is consistent with the single
stellar evolution scenario in which the star experienced a very late thermal
pulse instead of a nova-like event as previously suggested.
