Awk with Multiple files

Hello,

I wanted to know the best way to do some matching between two files. I am currently using awk.

Example Question: If column 4 from file A is contained in column 1 from file B. Print the whole row from file A of mix of information from both files. i.e.

File A

chr1	1104384	1104467	hsa-mir-429
chr1	21314806	21314925	hsa-mir-1256
chr1	23189651	23189719	hsa-mir-4253
chr1	28833876	28834083	U17a

File B

name              start end acc
"hsa-mir-429-5p"	6 27	"MIMAT0000062"
"hsa-mir-429-3p"	57 77	"MIMAT0004481"
"hsa-mir-4253"	5 26	"MIMAT0000062"
"hsa-mir-1256-3p"	50 71	"MIMAT0010195"

Output

chr1	1104384	1104467	hsa-mir-429  "hsa-mir-429-5p"	6 27	"MIMAT0000062"
chr1	1104384	1104467	hsa-mir-429 "hsa-mir-429-3p"	57 77	"MIMAT0004481"
chr1	21314806	21314925	hsa-mir-1256 "hsa-mir-1256-3p"	50 71	"MIMAT0010195"
chr1	23189651	23189719	hsa-mir-4253 "hsa-mir-4253"    5 26	"MIMAT0000062"
perl -lane 'open I,"<fileB";for(<I>){@x=split/\s+/,$_;($x[0]=~/$F[3]/)&&print "@F @x"};close I' fileA