You can access vk api via http requests. For doing this you need access_token, read here how to get it if you dont have it already.
Then you way will be very easy by link
https://api.vk.com/method/wall.repost?object=WALL_OBJECT_HERE&group_id=TARGET_GROUP_ID&access_token=YOUR_ACCESS_TOKEN
If repost done successfully, you will see response like this:
{"response":{"success":1,"post_id":676,"reposts_count":3,"likes_count":11}}
But if you need to solve captcha response will be like this:
{"error":{"error_code":14,"error_msg":"Captcha needed","request_params":[{"key":"oauth","value":"1"},{"key":"method","value":"wall.repost"},{"key":"object","value":"your_object_here"},{"key":"group_id","value":"56983001"}],"captcha_sid":"381041951450","captcha_img":"http:\/\/api.vk.com\/captcha.php?sid=381041951450&s=1"}}
Now you can easily get captcha sid and captcha_img link, download it, solve and repeat request upper just with adding 2 parameters to it: captcha_key=YOUR_SOLVED_CAPTCHA&captcha_sid=SID_YOU_GOT
Success :)