We report on a measurement of the flavor-specific
B
0
s
lifetime and of the
D
−
s
lifetime using proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to
3.0
 
 
fb
−
1
of integrated luminosity. Approximately 407 000
B
0
s
→
D
(
*
)
−
s
μ
+
ν
μ
decays are partially reconstructed in the
K
+
K
−
π
−
μ
+
final state. The
B
0
s
and
D
−
s
natural widths are determined using, as a reference, kinematically similar
B
0
→
D
(
*
)
−
μ
+
ν
μ
decays reconstructed in the same final state. The resulting differences between widths of
B
0
s
and
B
0
mesons and of
D
−
s
and
D
−
mesons are
Δ
Γ
(
B
)
=
−
0.0115
±
0.0053
(
stat
)
±
0.0041
(
syst
)
 
 
ps
−
1
and
Δ
Γ
(
D
)
=
1.0131
±
0.0117
(
stat
)
±
0.0065
(
syst
)
 
 
ps
−
1
, respectively. Combined with the known
B
0
and
D
−
lifetimes, these yield the flavor-specific
B
0
s
lifetime,
τ
fs
B
0
s
=
1.547
±
0.013
(
stat
)
±
0.010
(
syst
)
±
0.004
(
τ
B
)
 
 
ps
and the
D
−
s
lifetime,
τ
D
−
s
=
0.5064
±
0.0030
(
stat
)
±
0.0017
(
syst
)
±
0.0017
(
τ
D
)
 
 
ps
. The last uncertainties originate from the limited knowledge of the
B
0
and
D
−
lifetimes. The results improve upon current determinations.