no they can not be used in the same gun you would need a different barrel Parent case
.22 WRF
Bullet diameter
.224 in (5.7 mm)
Neck diameter
.242 in (6.1 mm)
Base diameter
.242 in (6.1 mm)
Rim diameter
.294 in (7.5 mm)
Rim thickness
.050 in (1.3 mm)
Case length
1.055 in (26.8 mm)
Overall length
1.350 in (34.3 mm)
Rifling twist
1-16"
Primer type
Rimfire
17 HMR Parent case
.22 WMR
Bullet diameter
.172 in (4.4 mm)
Neck diameter
.190 in (4.8 mm)
Shoulder diameter
.238 in (6.0 mm)
Base diameter
.238 in (6.0 mm)
Rim diameter
.286 in (7.3 mm)
Case length
1.058 in (26.9 mm)
Overall length
1.349 in (34.3 mm)
Primer type
Rimfire
You could probably fire a 17 HMR in a 22WMR chamber but you may have split cases and there would be zero accuracy and serious safety considerations

No Lewis. The 17 caliber HMR is based off of the 'Necked Down" 22 Magnum case but the projectiles themselves are not to be fired from the same chamber. You will have to use a dedicated 22Mag or dedicated 17HMR barrel for each cartridge.