Correct and transform SRID with PostGIS

gistfile1.sql

-- add temporary column for storing geometry with correct SRID
select AddGeometryColumn('places', 'geom_4301', 4301, 'GEOMETRY', 2);
-- add temporary column for storing geometry with target SRID
select AddGeometryColumn('places', 'geom_4326', 4326, 'GEOMETRY', 2);

BEGIN;

-- set the source temporary column with geometries with corrected SRID
UPDATE places SET geom_4301 = 'SRID=4301;POINT('|| ST_X(geom) || ' ' || ST_Y(geom) || ')';

-- transform SRID to target temporary column
UPDATE places SET geom_4326 = ST_Transform(geom_4301, 4326);

-- move the newly corrected & transformed geometries to the original geometry column
UPDATE places p SET geom = geom_4326;

COMMIT;

-- remove temporary columns
select DropGeometryColumn('places', 'geom_4301');
select DropGeometryColumn('places', 'geom_4326');