While I don't think that there is a general solution to this problem. Here is an expample of a very hard case.

package A;

use Data::Dumper ();
sub Dumper {
    print "This is not dumper\n";
}
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However if you make some assumptions you can get something that works (or gets close to it).

package ibase;

BEGIN {
    require base;

    *{"_import"} = \&{"base::import"};
    for (qw( )) {
        *{"$_"} = \&{"base::$_"};
    }
}

our $ExportLevel = 0;

sub import
{
    my $self = shift;

    my $callpkg = caller($ExportLevel);

    eval {
        $self->_import(@_);
    };
    for my $key (keys %INC) {
        if ($key =~ m|Data/Dumper.pm|) {
            *{"$callpkg\::Dumper"} = \&{"Data::Dumper::Dumper"};
        }
    }
}
1;
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Then use ibase rather than base.

package A;
use Data::Dumper;
print Dumper \%INC, \@INC;

package B;
use strict;

use ibase 'A';
print Data::Dumper::Dumper(\%A::INC, \%INC);
print Dumper([1]);
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You code make this a little more robust buy using @EXPORT_OK to see what all should be imported.