  We study environmental quenching using the spatial distribution of current
star-formation and stellar population ages with the full SAMI Galaxy Survey. By
using a star-formation concentration index [C-index, defined as
log10(r_{50,Halpha}/r_{50,cont})], we separate our sample into regular galaxies
(C-index>-0.2) and galaxies with centrally concentrated star-formation
(SF-concentrated; C-index<-0.2). Concentrated star-formation is a potential
indicator of galaxies currently undergoing `outside-in' quenching. Our
environments cover ungrouped galaxies, low-mass groups (M_200<10^12.5 M_sun),
high-mass groups (M_200 in the range 10^{12.5-14} M_sun) and clusters
(M_200>10^14 M_sun). We find the fraction of SF-concentrated galaxies increases
as halo mass increases with 9\pm2 per cent, 8\pm3 per cent, 19\pm4 per cent and
29\pm4 per cent for ungrouped galaxies, low-mass groups, high-mass groups and
clusters, respectively. We interpret these results as evidence for `outside-in'
quenching in groups and clusters. To investigate the quenching time-scale in
SF-concentrated galaxies, we calculate light-weighted age (Age_L) and
mass-weighted age (Age_M) using full spectral fitting, as well as the Dn4000
and Hdelta_A indices. We assume that the average galaxy age radial profile
before entering a group or cluster is similar to ungrouped regular galaxies. At
large radius (1-2 R_e), SF-concentrated galaxies in high-mass groups have older
ages than ungrouped regular galaxies with an age difference of 1.83\pm0.38 Gyr
for Age_L and 1.34\pm0.56 Gyr for Age_M. This suggests that while `outside-in'
quenching can be effective in groups, the process will not quickly quench the
entire galaxy. In contrast, the ages at 1-2 R_e of cluster SF-concentrated
galaxies and ungrouped regular galaxies are consistent (0.19\pm0.21 Gyr for
Age_L, 0.40\pm0.61 Gyr for Age_M), suggesting the quenching process must be
rapid.
