Context :

Aims : A super-solar fluorine abundance was observed in the carbon-enhanced metal-poor ( CEMP ) star HE 1305+0132 ( [ F/Fe ] = + 2.90 , [ Fe/H ] = - 2.5 ) .
We propose that this observation can be explained using a binary model that involve mass transfer from an asymptotic giant branch ( AGB ) star companion and , based on this model , we predict F abundances in CEMP stars in general .
We discuss wether F can be used to discriminate between the formation histories of most CEMP stars : via binary mass transfer or from the ejecta of fast-rotating massive stars .

Methods : We compute AGB yields using different stellar evolution and nucleosynthesis codes to evaluate stellar model uncertainties .
We use a simple dilution model to determine the factor by which the AGB yields should be diluted to match the abundances observed in HE 1305+0132 .
We further employ a binary population synthesis tool to estimate the probability of F-rich CEMP stars .

Results : The abundances observed in HE 1305+0132 can be explained if this star accreted 3-11 % of the mass lost by its former AGB companion .
The primary AGB star should have dredged-up at least 0.2 { M } _ { \odot } of material from its He-rich region into the convective envelope via third dredge-up , which corresponds to AGB models of Z \simeq 0.0001 and mass \simeq 2 { M } _ { \odot } .
Many AGB model uncertainties , such as the treatment of convective borders and mass loss , require further investigation .
We find that in the binary scenario most CEMP stars should also be FEMP stars , that is , have [ F/Fe ] > +1 , while fast-rotating massive stars do not appear to produce fluorine .
We conclude that fluorine is a signature of low-mass AGB pollution in CEMP stars , together with elements associated with the slow neutron-capture process .

Conclusions :