Yes, the hub is identical
Same 4x100 PCD and same 54.1 mm centre bore: wheels from Triumph Acclaim bolt on and centre on Kia Picanto III without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from Triumph Acclaim is compared with the one from Kia Picanto III of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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≈5Jx13 ET45 · 165/70R13 — Check on the car
Compared with the original 4.5Jx13 ET41 on Kia Picanto III: shock absorber side +10.4 mm, wheel arch side +2.4 mm, tyre diameter −2.9 % : fit it with the original tyre size of Kia Picanto III (155/80R13), not that of Triumph Acclaim.
Comparison for guidance only (estimated width). Check in detail
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of Kia Picanto III (M12x1.5), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from Kia Picanto III on Triumph Acclaim?