Parental Leave - changing job

Was just wondering......

If you take some parental leave in your current job (or none at all), and you move to another company, are you entitled to the rest of your parental leave in the new company? Does the old company have to give the new place proof of the leave taken or not taken?

Thanks,

Mr Ed

Here are below the rules of parental leave

Generally you must have been working for the new employer for a year before you are entitled to parental leave. However if your child is very near the age threshold and you have been working for the new employer for more than three months but less than 1 year you are entitled to pro-rata parental leave. This is one week's leave for every month of employment completed.
If you change job and have used part of your parental leave allowance you can use the remainder after one year's employment with your new employer provided your child is still under the qualifying age
You must give written notice to your employer of your intention to take parental leave. You should inform your employer in writing at least six weeks before the leave is due to start. The notice should state the starting date and how long the leave will last. After this not less than four weeks before the leave is due to start, you will need to sign a document with your employer confirming the details of the leave.
Apart from a refusal on the grounds on non-entitlement, an employer may also postpone the leave for up to 6 months. This must be done before the confirmation document is signed. Grounds for such a postponement include lack of cover or the fact that other employees are already on parental leave. Normally only one postponement is allowed.
Employers must keep records of all parental leave taken by their employees. These records must include the period of employment of each employee and the dates and times of the leave taken. Employers must keep these records for 8 years. If an employer fails to keep records they may be liable to a fine of up to 2000 euro.
You are entitled to return to your job after your parental leave unless it is not reasonably practicable for the employer to allow you to return to your old job. If this is the case you must be offered a suitable alternative on terms no less favourable compared with the previous job including