[SalesForce] How to pass the Value from One VF page to another Page without using URL param

I'm trying to pass the value from a page variable to another page (both using different controller) without using parameters.

This is what am working on that.

I have user search page with input field.

It's a user search,If the user not found in the search, i provide the link below and says that click here to register. The input field search value which i have give should be populated in the Another page.

To achieve this how to pass the value, Please help me on this.

Page 1:

<apex:page controller="SearchPageController" sidebar="false" showHeader="false" docType="html-5.0" cache="false" id="pg">
<style>
    .slds-scope .slds-box {
    padding: 2rem;
    border-radius: 1.25rem;
    border: 4px solid #a4bfe4;
    width: 100%;
    padding-left: 55px;
    padding-right: 55px;
    margin: 0 auto;        
    background-color: #fdfdfd;
    } 
    .searchBox{
    border: 2px solid #a4bfe4;   
    border-radius: 1.25rem;
    padding-left: 5px;
    width: 25%;
    height : 30%;
    }

    .controls{
    background-color:#fdfdfd;
    }
</style>
<apex:form id="fm">

    <script>

    function conRec () {
        //  alert('conRec');
        var pattern = /^\w+@[a-zA-Z_]+?\.[a-zA-Z]{2,3}$/;
        var SearchVal = document.getElementById('pg:fm:pb:SearchValue').value;
        alert(SearchVal);
        if(SearchVal.match(pattern)){
            alert('true');
        }else{
            alert('False');
        }
    }
    </script>

    <apex:slds />
    <apex:pageBlock id="pb" >


        <div class="slds-scope slds-box">
            <apex:outputPanel >                   
                <div id="formBlock">

                    <div id="showErrorMsgbuserName">
                        <div class="slds-form-element">
                            <div class="slds-align_absolute-center">
                                <!--- <apex:input value="{!searchBoxstring}"  id="SearchID" styleClass="searchBox"/>  --->

                                <apex:input value="{!searchBoxstring}" styleClass="searchBox" id="SearchValue" />
                                &nbsp;  &nbsp;  &nbsp; <apex:commandButton value="Search" onClick="conRec()" action="{!display}"   >

                                </apex:commandButton>
                                <div class="slds-hide slds-form-element__help" id="error-message-userName">This field is required</div>
                            </div> 
                        </div>
                    </div>

                </div>

                <apex:pageMessages id="Error" escape="false" />


                <br/>
                <br/>    
                <apex:dataTable value="{!result}" var="con" border="1" cellpadding="5" cellspacing="4" bgcolor="lightblue">
                    <apex:column value="{!con.Name}" styleClass="controls">
                        <apex:facet name="header">Name</apex:facet>
                    </apex:column>
                    <apex:column value="{!con.Email}" styleClass="controls">
                        <apex:facet name="header">Email</apex:facet>
                    </apex:column>
                    <apex:column value="{!con.Phone}" styleClass="controls">
                        <apex:facet name="header">Phone</apex:facet>
                    </apex:column>
                </apex:dataTable>                   

            </apex:outputPanel>   
        </div>
    </apex:pageBlock>    


</apex:form>
</apex:page> 

Controller:

public class SearchPageController {

public string searchboxstring{get; set;}
public String Email{get;set;}

public list<contact> result {get; set;}

public SearchPageController()
{
    result = new list<Contact>();
}

public pagereference display(){
    system.debug('searchboxstring1-->' + searchboxstring);
    Email = searchboxstring;        
    result=new List<Contact>();
    system.debug('searchboxstring-->' + searchboxstring);
    Email = searchboxstring;
    system.debug('Email-->' + Email);
    //result=[select ID, Name, Email, Phone  from Contact where FirstName like :searchboxstring or LastName  like :searchboxstring or Email like :searchboxstring or Phone like :searchboxstring];
    result=[select ID, Name, Email, Phone  from Contact where Name like :searchboxstring or Email like :searchboxstring or Phone like :searchboxstring];
    system.debug('result-->' + result.size());
    if (result.size() < 1) {            
        ApexPages.addmessage(new ApexPages.message(ApexPages.Severity.ERROR,'No data Found' + '<a href='+ System.URL.getSalesforceBaseUrl().toExternalForm()+ '/apex/Registration' + '>Click Here</a>' + 'to Register  Or '+ '<a href='+ System.URL.getSalesforceBaseUrl().toExternalForm()+ '/apex/Registration' + '>Click Here</a>' +' to Send Email to Register'));
    }

    return null;

}
}